Midterm Mcqs
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
1. While finding RE corresponding to TG, we connect the new start state to the old start
state by the transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b.
(ba+a)* c.
a*(aa*b)* d. (a*b*)*
a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*.
{ x}*, { x}+, {a+b}*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must
correspond to
the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Question No: 1 ( Marks: 1 ) - Please choose one
Σ={a,Aa,Abb}, then string aAaAbbAa has ________ length.
► One
► Two
► Three
► Four
Question No: 2 ( Marks: 1 ) - Please choose one
Languages generated by kleene star are always ______________.
► Finite
► Infinite
► Sometimes finite & sometimes infinite
► None of the these
Question No: 3 ( Marks: 1 ) - Please choose one
Let
S = {aa, bb} be a set of strings then s* will have
►Λ
► abba
► aabbbaa
► bbaab
Question No: 4 ( Marks: 1 ) - Please choose one
If r1
= (aa + bb) and r2 = ( a + b) then the language (aa + bb)* will be generated by
► (r1)(r2)
► (r1 + r2)
► (r2)*
► (r1)*
Question No: 5 ( Marks: 1 ) - Please choose one
y
a, b
x±
a, b
Above given FA can be represented by
► ((a+ b) (a + b))*
► (a + b)(a + b)*
► (a + b)(a + b)
► (a + b)*(a + b)*
Question No: 6 ( Marks: 1 ) - Please choose one
a,b
2+
1± a,b
Above given FA accepts ___________ strings defined over Σ={a , b}
► All
► Some
► All but not null
► None of these
Question No: 7 ( Marks: 1 ) - Please choose one
If a
language can be expressed through FA, then it can also be expressed through TG.
► True
► False
► Depends on language
► None of the above
Question No: 8 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given TG has ____________________ RE.
► a+b+a(a + b)*a + b(a + b)*b
► a(a + b)*a + b(a + b)*b
► both are given
► none of the given
Question No: 9 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given FA accepts the language in which strings
► Begins with and ends in same letter
► Begins with and ends in different letter
► Has length more than 2
► None of the given
Question No: 10 ( Marks: 1 ) - Please choose one
GTG can have _______________ final state.
►0
►1
► More than 1
► All of the given
Question No: 11 ( Marks: 1 ) - Please choose one
In
GTG, if a state has more than one incoming transitions from a state. Then all those
incoming
transitions can be reduced to one transition using _____________ sign
►►+
►*
► None of the given
Question No: 12 ( Marks: 1 ) - Please choose one
aa+bb
ab+ba
ab+ba
aa+bb
Λ
4+
3- 1 2
Λ
If above given TG is drawn like
aa+bb
Λ
4
31
Λ
X
Then what will be written in place of X.
► (ab+ba)(aa+bb)(ba+ab)
► (ab+ba)(aa+bb)(ab+ba)
► (ab+ba)(aa+bb)*(ab+ba)
► (ab+ba)(aa+bb)(ab+ba)*
Question No: 13 ( Marks: 1 ) - Please choose one
“One language can be expressed by more than one NFA”. This statement is
______________.
► False
► True
► Depends on NFA
► None of the given
Question No: 14 ( Marks: 1 ) - Please choose one
a
^
1-
4+
b5
aa
a
^, b
a
2
3
Above given structure is an ________.
► FA
► NFA
► NFA -^
► TG
Question No: 15 ( Marks: 1 ) - Please choose one
One
FA has 3 states and 2 letters in the alphabet. Then FA will have ___________
number of
transitions in the diagram
►4
►5
►7
►6
Question No: 16 ( Marks: 1 ) - Please choose one
aa
b
bb
a
123+
4+
b
a
Above given two TG’s are _______________.
► Equivalent
► None-equivalent
► Not valid
► None of the given
Question No: 17 ( Marks: 1 )
What do you mean by dead state?
Question No: 18 ( Marks: 1 )
Define empty or null strings?
Question No: 19 ( Marks: 2 )
Write strings that ends on "a" and strings containing exactly one "a". over Σ= {a, b}
Question No: 20 ( Marks: 3 )
Let
S be all string of a’s and b’s with odd length. What is S*?
Question No: 21 ( Marks: 5 )
Give the transition table of an FA3 corresponding to FA1+FA2, where FA1, FA2 are
given below.
FA1
FA2
Q1
A DFA with n states must accept at least one string of length greater than n.
Choices:
True
False
Q2
FA corresponding to an NFA can be built by introducing a state corresponding to the
combination of states, for a letter having
Choices:
no transition at certain state
one transition at certain state
more than one transitions at certain state
none of the given options
Q3
Which of the following statement is NOT true?
Choices:
1. FA can be considered to be an NFA
2. FA can be considered to be an NFA with null string
3. NFA can be considered to be an TG
4. TG can be considered to be an NFA
Q4
For every three regular expressions R, S, and T, the languages denoted by R(S U T) and
(RS) U
(RT) are the same.
Choices:
1. True
2. False
Q5
Does the empty string match the regular expression |y+a|?
Choices:
1. Yes
2. No
Q6
If an FA already accepts the language expressed by the closure of certain RE, then the
given FA
is the required FA.
Choices:
1. True
2. False
Q7
Which of the following statement is true about NFA with Null String?
Choices:
1. Infinite states
2. Infinite set of letters
3. Infinite set of transitions
4. Transition of null string is allowed at any stage
Q8
If R is a regular language and L is some language, and L U R is a regular language, then
L must
be a regular language.
Choices:
1. True
2. False
Q9
FA corresponding to an NFA can be built by introducing an empty state for a letter
having
Choices:
1. no transition at certain state
2. one transition at certain state
3. two transition at certain state
4. more than two transitions at certain state
Q10
Let FA3 be an FA corresponding to FA1FA2, then the initial state of FA3 must
correspond to the
initial state of
Choices:
1. FA1 only
2. FA2 only
3. FA1 or FA2
4. FA1 and FA2
FAs is an FA that accepts all the string of FA1 andFA2. Union of two
True
False
A production of the form non-terminal string of two non-terminal is called a live
Production.
True
False
DFA and PDA are equal in power.
True
False
4:
Syntax tree or Generation tree or Derivation tree are same tree
true
false
5;
PDA is only used to represent a regular language.
True
False
6:
PDA is stronger than FA.
True
False
7:
Two FAs are equivalent if they have same no. of states.
ture
false
8:
There exist exactly two different derivations in an ambiguous CFG for a word.
true
false
Length of EVEN-EVEN language is _________
1. even
2. odd
3. sometimes even n sometimes odd
4. no such language
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be
generated
by
1. (r1)(r2)
2. (r1 + r2)
3. (r2)(r1)
4. (r1)*
What is false about the term alphabet?
1. It is a finite set of symbols.
2. It is usually denoted by Greek letter sigma
3. It can be an empty set.
4. Strings are made up of its elements.
If S = {ab, bb}, then S* will not contain
1. abbbab
2. bbba
3. bbbbab
4. ababbb
If S = { x }, then S* will be
1. {x,xx,xxx,xxxx,…}
2. {^ ,x,xx,xxx,xxxx,…}
Let FA3 be an FA corresponding to FA1+FA2, then the final state of FA3 must
correspond to the final state of
1. FA1 only
2. FA2 only (not confirmed)
3. both
4. FA1 or FA2
a* + b* = (a + b)* this expression is _________
1. true
2. false
Alphabet S = {a, bc, cc} has _______ number of letters
1. one
2. two
3. three
4. four
Which of the following statement is NOT true about TG?
1. There exists exactly one path for certain string
2. There may exist more than one paths for certain string
3. There may exist no path for certain string
4. There may be no final state
What do automata mean?
1. Something done manually
2. Something done automatically
The states in which there is no way to leave after entry are called
1. Davey John Lockers
2. Dead States
3. Waste Baskets
4. All of the given options
Which of the following regular expression represents same language? a.
(a+ab)* b.
(ba+a)* c. a*(aa*b)* d. (a*b*)*
1. a and b
2. a and c
3. c and d
4. All of the given options
5. nahi pata
If two RE’s generate same language then these RE’s are called
1. Same RE
2. Equal RE
3. Similar RE
4. Equivalent RE
Given S, Kleene star closure is denoted by
1. S*
2. S+
3. S4. None of these
To obtain an RE corresponding to the given TG , TG is converted into
1. FA
2. GTG
3. NFA
4. none of given
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
1. Introduce the new start state
2. Eliminate the old start state
3. Replace the old start state with final state
4. Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start
state by the transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b.
(ba+a)* c. a*(aa*b)* d. (a*b*)*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must
correspond to the initial state of
Select correct option:
1. FA1 only
2. FA2 only
3. FA1 or FA2
4. FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
1. There exists exactly one path for certain string
2. There may exist more than one paths for certain string
3. There may exist no path for certain string
4. There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 ( Start time: 05:55:36 PM ) Total Marks: 1
What do automata mean?
Select correct option:
1. Something done manually
2. Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question No: 1 ( Marks: 1 ) - Please choose one
Σ={a,Aa,Abb}, then string aAaAbbAa has ________ length.
► One
► Two
► Three
► Four
Question No: 2 ( Marks: 1 ) - Please choose one
Languages generated by kleene star are always ______________.
► Finite
► Infinite
► Sometimes finite & sometimes infinite
► None of the these
Question No: 3 ( Marks: 1 ) - Please choose one
Let
S = {aa, bb} be a set of strings then s* will have
►Λ
► abba
► aabbbaa
► bbaab
Question No: 4 ( Marks: 1 ) - Please choose one
If r1
= (aa + bb) and r2 = ( a + b) then the language (aa + bb)* will be generated by
► (r1)(r2)
► (r1 + r2)
► (r2)*
► (r1)*
Question No: 5 ( Marks: 1 ) - Please choose one
y
a, b
x±
a, b
Above given FA can be represented by
► ((a+ b) (a + b))* ► (a + b)(a + b)*
► (a + b)(a + b)
► (a + b)*(a + b)*
Question No: 6 ( Marks: 1 ) - Please choose one
a,b
2+
1± a,b
Above given FA accepts ___________ strings defined over Σ={a , b}
► All
► Some
► All but not null
► None of these
Question No: 7 ( Marks: 1 ) - Please choose one
If a
language can be expressed through FA, then it can also be expressed through TG.
► True
► False
► Depends on language
► None of the above
Question No: 8 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given TG has ____________________ RE.
► a+b+a(a + b)*a + b(a + b)*b
► a(a + b)*a + b(a + b)*b
► both are given
► none of the given
Question No: 9 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given FA accepts the language in which strings
► Begins with and ends in same letter
► Begins with and ends in different letter
► Has length more than 2
► None of the given
Question No: 10 ( Marks: 1 ) - Please choose one
GTG can have _______________ final state.
►0
►1
► More than 1
► All of the given
Question No: 11 ( Marks: 1 ) - Please choose one
In
GTG, if a state has more than one incoming transitions from a state. Then all those
incoming
transitions can be reduced to one transition using _____________ sign
►►+
►*
► None of the given
Question No: 12 ( Marks: 1 ) - Please choose one
aa+bb
ab+ba
ab+ba
aa+bb
Λ
4+
3- 1 2
Λ
If above given TG is drawn like
aa+bb
Λ
4
31
Λ
X
Then what will be written in place of X.
► (ab+ba)(aa+bb)(ba+ab)
► (ab+ba)(aa+bb)(ab+ba)
► (ab+ba)(aa+bb)*(ab+ba)
► (ab+ba)(aa+bb)(ab+ba)*
Question No: 13 ( Marks: 1 ) - Please choose one
“One language can be expressed by more than one NFA”. This statement is
______________.
► False
► True
► Depends on NFA
► None of the given
Question No: 14 ( Marks: 1 ) - Please choose one
a
^
1-
4+
b5
aa
a
^, b
a
2
3
Above given structure is an ________.
► FA
► NFA
► NFA -^
► TG
Question No: 15 ( Marks: 1 ) - Please choose one
One
FA has 3 states and 2 letters in the alphabet. Then FA will have ___________
number of
transitions in the diagram
►4
►5
►7
►6
Question No: 16 ( Marks: 1 ) - Please choose one
aa
b
bb
a
123+
4+
b
a
Above given two TG’s are _______________.
► Equivalent
► None-equivalent
► Not valid
► None of the given
True or False
1. In a finite language no string is pumpable. True
2. A DFA has infinite number of states. False
3. A DFA can have more than one accepting state. True
4. In DFA all states have same number of transitions. True
5. Every subset of a regular language is regular. False
6. Let L4 = L1L2L3. If L1 and L2 are regular and L3 is not regular, it is possible that L4
is
regular. True
7. In a finite language no string is pumpable. True
8. If A is a nonregular language, then A must be infinite. True example palendroms
9. Every context-free language has a context-free grammarin Chomsky normal form.
True
10. If A is a context-free language, then A must be nonregular. False
11. The class of regular languages is closed under intersection. True
12. If a language A is regular, then it A must be finite. False
13. Every language is Turing-recognizable. False
14. If a language is context-free, then it must be Turing-decidable. True
15. The problem of determining if a context-free grammar generates
the empty language is undecidable. False
16. The problem of determining if a Turing machine recognizes the
empty language is undecidable. True
17. The set of all languages over an alphabet is countable.False
18. There are some languages recognized by a 5-tape, nondeterministic
Turing machine that cannot be recognized by a 1-tape,
deterministic Turing machine.False
19. The language { 0n1n | 0 ≤ n ≤ 1000 } is regular. True
20. Nonregular languages are recognized by NFAs. False
21. The class of context-free languages is closed under intersection. False
22. A language has a regular expression if and only if it
has an NFA. True
23. The regular expression (01*0 ∪ 1)*0 generates the language
consisting of all strings over {0, 1} having
an odd number of 0’s. False
24. If a language A has a PDA, then A is generated by a
context-free grammar in Chomsky normal form. True
25. If A is a context-free language and B is a language such that B is a subset of A, then
B
must be a context-free language. False
26. If a language A has an NFA, then A is nonregular. False
27. The regular expressions (a ∪ b)* and (b*a*)* generate the same language. True
28. If a language A has a regular expression, then it also has a context-free grammar.
True
Regular Expressions
Describe the language denoted by the following regular expressions:
a) a(a|b)*a
The expression denotes the set of all strings of length two or more that start and end with
an ‘a’.
b) ((e|a)b*)*
The expression denotes the set of all strings over the alphabet {a,b}.
c) (a|b)*a(a|b)(a|b)
The expression denotes the set of all strings of length 3 or more with an ‘a’ in the third
position
from the right. Ie of form yaxz where y is an arbitrary string , and x and z are single
characters.
d) a*ba*ba*ba*
The expression denotes the set of all strings that contain precisely 3 b’s.
e) (aa|bb)*((ab|ba)(aa|bb)*(ab|ba)(aa|bb)*)*
The expression denotes the set of all strings of even length.
Length of a null string is supposed to be 1.
► True
► False
There is no difference between Word and String
► True
► False
There may be two RE representing the same language.
► True
► False
NFA – null can be considered as TG and vise versa.
► True
► False
Σ = {aA, b}, length(aAbaAaAb) = 5.
► True
► False
If s=abcd is a string defined over Σ = {a,b,c,d} then reverse of s is dcba.
► True
► False
The language equal means number of a’s and b’s are equal with no null string.
► True
► False
Palindrome is a regular language.
► True
► False
If s = babab then palindrome of s = rev(s).
► True
► False
TG must have only one start state.
► True
► False
If a language can be accepted by FA then it can be accepted by a TG as well.
► True
► False
Length of output string is 1 less then that of input string is mealy machine.
► True
► False
Formal languages are called Semantic languages.
► True
► False
Every NFA can be converted to an FA
► True
► False
In mealy machine output character are mentioned on the transition.
► True
► False
If s=abcd is a string defined over Σ = {a,bc,d} then reverse of s is dcba.
True
False
Σ = {aa, b}, length(aaaabaabb) = 5.
True
False
Every NFA can be converted into FA.
True
False
There can be more than one start states in TG.
True
False
A regular language can not be infinite.
True
False
Kleene star of {1} generates {1, 11, 111, 1111, 11111 ……}.
True
False
If a regular language is empty then we denote it like L = Ǿ (fi).
True
False
Recursive method for defining language is only for regular languages.
True
False
Aa* = a +?
True
False
The language equal means number of a’s and b’s are equal with null string.
True
False
PDA is only used to represent a regular language.
► True
► False
Question No: 2 ( Marks: 1 ) - Please choose one
If L is a regular language then LC is also a regular language.
► True
► False
Question No: 3 ( Marks: 1 ) - Please choose one
A production of the form non-terminal Æ string of two non-terminal is called a live
Production.
► True
►False
Question No: 4 ( Marks: 1 ) - Please choose one
we can find a CFG corresponding to a DFA.
► True
► False
Question No: 5 ( Marks: 1 ) - Please choose one
START, READ, HERE and ACCEPTS are conversions of the machine
(these are joints of machine)
► True
► False
Question No: 6 ( Marks: 1 ) - Please choose one
A CFG is said to be ambiguous if there exists at least one word of its language that can
be generated by different production trees
► True
► False
Syntax tree or Generation tree or Derivation tree are same tree
► True
► False
Question No: 8 ( Marks: 1 ) - Please choose one
The symbols that cannot be replaced by anything are called terminals
► True
► False
Question No: 9 ( Marks: 1 ) - Please choose one
The production of the form non-terminal Æ one non-terminal is called unit production
► True
► False
Question No: 10 ( Marks: 1 ) - Please choose one
DFA and PDA are equal in power.
► True
► False
Question No: 10 ( Marks: 1 ) - Please choose one
DFA and PDA are equal in power.
► True
► False
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start
state by the
transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language?
a. (a+ab)*
b. (ba+a)*
c. a*(aa*b)*
d. (a*b*)*
a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*.
{ x}*, { x}+, {a+b}*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must
correspond to
the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Alphabet S = {a, bc, cc} has _______ number of letters
1. One
2. Two
3. Three
4. Four
If S = { x }, then S* will be
1. {x,xx,xxx,xxxx,…}
2. {^ ,x,xx,xxx,xxxx,…}
Length of even even language is
1. Even
2. Odd
3. Sometimes even & sometimes odd
4. Such languages does not exist
If S = {aa, bb}, then S* will not contain
1. Aabbaa
2. Bbaabbbb
3. Aaabbb
4. aabbaaaa
Formal is also known as _________
1. Syntactic language
2. Semantic language
3. Informal language
4. None of these
In an FA, when there is no path starting from initial state and ending in final state then that FA
1. accept null string
2. accept all strings
3. accept all non empty strings
4. does not accept any string
FA of EVEN language shows null string when
1. Initial state is final as well
2. EVEN does not accept null
3. One state is declared null
4. None of the these
Find the regular expression associated to the following FA. Show all steps. [Hint: use FA
to GTG and GTG
to RE.]
Question No. 3 Marks :
Σ = {aa, b}, length(aaaabaabb) = 5.
� True
� False
Question No. 4 Marks :
Every NFA can be converted into FA.
� True
� False
Question No. 5 Marks :
There can be more than one start states in TG.
� True
� False
Question No. 6 Marks :
A regular language can not be infinite.
� True
� False
Question No. 7 Marks :
a) Write the recursive definition of the following language. [6]
L = Defining the language {a2n b4n }, n=1,2,3,… , of strings defined over Σ={a,
b}
b) Write a regular expression of the language having strings that either start or end with
“00” and have no more zeroes. Where the alphabet is {0, 1}. [4]
Question No. 8 Marks :
Kleene star of {1} generates {1, 11, 111, 1111, 11111 ……}.
� True
� False
Question No. 9 Marks :
a) Define NFA-null.
[4
]
b) Draw DFA for the following NFA.
[
6]
Question No. 10 Marks :
If a regular language is empty then we denote it like L = Ǿ (fi).
� True
� False
Question No. 11 Marks :
Recursive method for defining language is only for regular languages.
� True
� False
Question No. 12 Marks :
aa* = a+ ?
� True
� False
Question No. 13 Marks :
The language equal means number of a’s and b’s are
equal with null string. � True
� False
Length of a null string is supposed to be 1.
► True
► False
Question No: 2 ( Marks: 1 ) - Please choose one
There is no difference between Word and String
► True
► False
Question No: 3 ( Marks: 1 ) - Please choose one
There may be two RE representing the same language.
► True
► False
Question No: 4 ( Marks: 1 ) - Please choose one
NFA - null can be considered as TG and vise versa.
► True
► False
Question No: 5 ( Marks: 1 ) - Please choose one
Σ = {aA, b}, length(aAbaAaAb) = 5.
► True
► False
Question No: 6 ( Marks: 1 ) - Please choose one
If s=abcd is a string defined over Σ = {a,b,c,d} then reverse of s is dcba.
► True
► False
Question No: 7 ( Marks: 1 ) - Please choose on
The language equal means number of a’s and b’s are equal with no null string.
► True
► False
Question No: 8 ( Marks: 1 )
Palindrome is a regular language.
► True
► False
Question No: 9 ( Marks: 1 )
- Please cho
- Please cho
If s = babab then palindrome of s = rev(s).
► True
► False
Question No: 10 ( Marks: 1 )
TG must have only one start state.
► True
► False
Question No: 11 ( Marks: 1 )
- Please ch
- Please ch
If a language can be accepted by FA then it can be accepted by a TG as well.
► True
► False
Question No: 12 ( Marks: 1 ) - Please choose one
Length of output string s 1 less then that of input string is mealy machine.
► True
► False
Question No: 13 ( Marks: 1 ) - Please choose one
Formal languages are called Semantic languages.
► True
► False
Question No: 14 ( Marks: 1 ) - Please choose one
Every NFA can be converted to an FA
► True
► False
Question No: 15 ( Marks: 1 ) - Please choose one
In mealy machine output character are mentioned on the transition.
► True
► False
Question No: 16 ( Marks: 8 )
Differentiate between the following terms:
• Mealy and Moore machine.
• NFA and FA.
Question No: 17 ( Marks: 5 )
Build an FA corresponding to NFA given below.
q1 b
a
b
q0 +q3
Question No: 18 ( Marks: 7 )
Build an NFA equivalent to FA1U FA2, where FA1, FA2 are given below.
FA1
b
pa
q
b
3
FA2
2a4
a b a a,b
1- a b 6+
bab
3b5
1) For a given input, it provides the compliment of Boolean AND output.
NAND box (NOT AND)
DELAY box
OR box
AND box
2) It delays the transmission of signal along the wire by one step (clock pulse).
NAND box (NOT AND)
DELAY box
OR box
AND box
3) For the given input, it provides the Boolean OR output
NAND box (NOT AND)
DELAY box
OR box
AND box
4) For the given input, AND box provides the Boolean AND output.
True False
5) The current in the wire is indicated by 1 and 0 indicates the absence of the
current.
True False
6) Any language that can not be expressed by a RE is said to be regular language.
True False
7) If L1 and L2 are regular languages is/are also regular language(s).
L1 + L2
L1L2
L1*
All of above
8) Let L be a language defined over an alphabet Σ, then the language of strings,
defined over
Σ, not belonging to L, is called Complement of the language L, denoted by Lc or L’.
True False
9) To describe the complement of a language, it is very important to describe the ---------- of
that language over which the language is defined.
Alphabet
Regular Expression
String
Word
10) For a certain language L, the complement of Lc is the given language L i.e. (Lc)c
= Lc
True False
11) If L is a regular language then, --------- is also a regular language.
Lm Ls Lx Lc
12) Converting each of the final states of F to non-final states and old non-final
states of F to
final states, FA thus obtained will reject every string belonging to L and will accept
every
string, defined over Σ, not belonging to L. is called
Transition Graph of L
Regular expression of L
Complement of L
Finite Automata of L
13) If L1 and L2 are two regular languages, then L1 U L2 is not a regular.
True False
14) De-Morgan's law for sets is expressed by,
1 2 1 2 (L c ∩L c )c = L c ∩L c
1 2 1 2 (L c ∩L c )c = L c ∩L c
1 2 1 2 (L c ∩L c )c = L ∩L
1 2 1 2 (L c ∩L c )c = L ∪L CORRECT
15) If L1 and L2 are regular languages, then these can be expressed by the
corresponding FAs.
True False
16) L= language of words containing even number of a’s. Regular Expression is
(a+b)*aa(a+b)*
(b+ab*a)*
a+bb*aab*a
(a+b)*ab(a+b)*
17) The regular expression defining the language L1 U L2 can be obtained,
converting and
reducing the previous ------------- into a ------------ as after eliminating states.
GTG, TG
FA, GTG
FA, TG
TG, RE
18) The language that can be expressed by any regular expression is called a Non
regular
language.
True False
19) The languages -------------- are the examples of non regular languages.
PALINDROME and PRIME
PALINDROME and EVEN-EVEN
EVEN-EVEN and PRIME
FACTORIAL and SQURE
20) Let L be any infinite regular language, defined over an alphabet Σ then there
exist three
strings x, y and z belonging to Σ* such that all the strings of the form xynz for
n=1,2,3, …
are the words in L. called.
Complement of L
Pumping Lemma
Kleene’s theorem
None in given
(21) Languages are proved to be regular or non regular using pumping lemma.
True False
(22) ------------------- is obviously infinite language.
EQUAL-EQUAL
EVEN-EVEN
PALINDROME
FACTORIAL
(23) If, two strings x and y, defined over Σ, are run over an FA accepting the
language L, then
x and y are said to belong to the same class if they end in the same state, no matter
that
state is final or not.
True False
(24) Myhill Nerode theorem is consisting of the followings,
L partitions Σ* into distinct classes.
If L is regular then, L generates finite number of classes.
If L generates finite number of classes then L is regular.
All of above
(25) The language Q is said to be quotient of two regular languages P and R,
denoted by--- if
PQ=R.
R=Q/P Q=R/P Q=P/R P=R/Q
(26) If two languages R and Q are given, then the prefixes of Q in R denoted by Pref(Q
in R).
True False
(27) Let Q = {aa, abaaabb, bbaaaaa, bbbbbbbbbb} and R = {b, bbbb, bbbaaa,
bbbaaaaa}
Pref (Q in R) is equal to,
{b,bbba,bbbaaa}
{b,bba,bbaaa}
{ab,bba,bbbaa}
{b,bba,bbba}
(27) If R is regular language and Q is any language (regular/ non regular), then Pref
(Q in
R) is ---------.
Non-regular
Equal
Regular
Infinite
(28) "CFG" stands for _________
Context Free Graph
Context Free Grammar
Context Finite Graph
Context Finite Grammar
(29) ___________ states are called the halt states.
ACCEPT and REJECT
ACCEPT and READ
ACCEPT AND START
ACCEPT AND WRITE
(30) The part of an FA, where the input string is placed before it is run, is called
_______
State
Transition
Input Tape
Output Tape
(31) In new format of an FA (discussed in lecture 37), This state is like dead-end non
final
state
ACCEPT
REJECT
STATR
READ
(32) For language L defined over {a, b}, then L partitions {a, b}* into …… classes
Infinite
Finite
Distinct
Non-distinct
(33) The major problem in the earliest computers was
To store the contents in the registers
To display mathematical formulae
To load the contents from the registers
To calculate the mathematical formula
(34) Between the two consecutive joints on a path
One character can be pushed and one character can be popped
Any no. of characters can be pushed and one character can be popped
One character can be pushed and any no. of characters can be popped
Any no. of characters can be pushed and any no. of characters can be popped
(35) In pumping lemma theorem (x y^n z) the range of n is
n=1, 2, 3, 4……….
n=0, 1, 2, 3, 4……….
n=…….-3,-2,-1, 0, 1, 2, 3, 4……
n=…….-3,-2,-1, 1, 2, 3, 4……
(36) The PDA is called non-deterministic PDA when there are more than one out
going
edges from……… state
START or READ
POP or REJECT
READ or POP
PUSH or POP
(37) Identify the TRUE statement:
A PDA is non-deterministic, if there are more than one READ states in PDA
A PDA is never non-deterministic
Like TG, A PDA can also be non-deterministic
A PDA is non-deterministic, if there are more than one REJECT states in PDA
(38) There is a problem in deciding whether a state of FA should be marked or not
when the
language Q is infinite.
True False
(39) If an effectively solvable problem has answered in yes or no, then this solution is
called -------Decision procedure
Decision method
Decision problem
Decision making
(40) The following problem(s) ------------- is/are called decidable problem(s).
The two regular expressions define the same language
The two FAs are equivalent
Both a and b
None of given
(41) To examine whether a certain FA accepts any words, it is required to seek the
paths
from ------- state.
Final to initial
Final to final
Initial to final
Initial to initial
(42) The high level language is converted into assembly language codes by a
program called
compiler.
TRUE FALSE
(43) Grammatical rules which involve the meaning of words are called --------------Semantics
Syntactic
Both a and b
None of given
(44) Grammatical rules which do not involve the meaning of words are called -------------Semantics
Syntactic
Both a and b
None of given
(45) The symbols that can’t be replaced by anything are called ----------------Productions
Terminals
Non-terminals
All of above
(46) The symbols that must be replaced by other things are called __________
Productions
Terminals
Non-terminals
None of given
(47) The grammatical rules are often called_____________
Productions
Terminals
Non-terminals
None of given
(47) The terminals are designated by ________ letters, while the non-terminals are
designated by ________ letters.
Capital, bold
Small, capital
Capital, small
Small, bold
(48) The language generated by __________ is called Context Free Language (CFL).
FA TG CFG TGT
(49) Σ = {a,b} Productions S→XaaX X→aX X→bX X→Λ
This grammar defines the language expressed by___________
(a+b)*aa(a+b)*
(a+b)*a(a+b)*a
(a+b)*aa(a+b)*aa
(a+b)*aba+b)*
(50) S → aXb|b XaX → aX|bX|Λ The given CFG generates the language in English
__________
Beginning and ending in different letters
Beginning and ending in same letter
Having even-even language
None of given
(51) The CFG is not said to be ambiguous if there exists atleast one word of its
language that
can be generated by the different production trees,
TRUE FALSE
(52) The language generated by that CFG is regular if _________
No terminal → semi word
No terminal → word
Both a and b
None of given
(53) The production of the form no terminal → Λ is said to be null production.
TRUE FALSE
(54) A production is called null able production if it is of the form N → Λ
TRUE FALSE
(55) The productions of the form nonterminal → one nonterminal, is called
_________
Null production
Unit production
Null able production
None of given
(56) CNF is stands for
Context Normal Form
Complete Normal Form
Chomsky Normal Form
Compared Null Form
The input string is placed, before it runs, in
1. Stack
2. Memory
3. Tape
4. Ram
Every nondeterministic finite automata can be converted into
1. Regular expression
2. Deterministic finite
3. Transition graph
4. All of the given option.
In CFG, the symbols that cannot be replaced by anything are called
1. Terminals
2. Nonterminals
3. Productions
4. None of the given options
If L1 and L2 are regular languages then which statement is NOT true?
1. L1 + L2 is always regular
2. L1 L2 is always regular
3. L1/L2 is always regular
4. L1* is always regular
The tree which produced all the strings of a language is called
1. Derivation tree
2. Ambiguous tree
3. Total language tree
4. Non ambiguous tree
By removing null and unit productions:
1. CNF can be converted into CFG
2. CFG can be converted into CNF
3. CNF can be converted into TG
4. None of the given options
Question: 31 (Marks 1)
Can you say that string of 0’s whose length is a perfect square is not regular?
Question: 32 (Marks 1)
Question: 33 (Marks 2)
Is the following an FA or TM?
Question: 34 (Marks 2)
If L is the language that accept even length strings then what strings will Lc accept?
Question: 35 (Marks 3)
Define Myhill Nerode theorem
Question: 36 (Marks 3)
If L1,L2 and L3 be any three finite languages over Sigma = {a,b}, then how will be
(L1 INTERSECTION L2) Union (L2 INTERSECTION L3) ≠ Ø
Question: 37 (Marks 3)
How you differentiate between wanted and unwanted branches while deriving a string
from in the
context of CFG?
Question: 38 (Marks 5)
What is the difference between concatenation and intersection of two FAs and union and
addition of two
FAs?
Question: 39 (Marks 5)
Use pumping lemma II to show that following language is not regular.
L = {an2 ; n =1,2,3,4…}
Question: 40 (Marks 10)
Draw Moore Machine equivalent to the following Mealy Machine.
Question: 41 (Marks 10)
Write CFG of the following PDA. Also write the stack alphabet and tape alphabet.
Question No: 1 ( Marks: 1 ) - Please choose one
If r1 = (aa +
bb) and r2 = ( a + b) then the language (aa + bb)(a + b) will be generated by
► (r1)(r2)
*► (r1 + r2)
► (r2)(r1)
► (r1)*
Question No: 2 ( Marks: 1 ) - Please choose one
“One
language can be expressed by more than one FA”. This statement is ______
* ► True
► False
► Some times true & sometimes false
► None of these
Question No: 3 ( Marks: 1 ) - Please choose one
Who did
not invent the Turing machine?
► Alan Turing
*► A. M. Turing
► Turing
► None of these
Question No: 4 ( Marks: 1 ) http://vustudents.ning.com - Please choose one
Which
statement is true?
*► The tape of turing machine is infinite.
► The tape of turing machine is finite.
► The tape of turing machine is infinite when the language is regular
► The tape of turing machine is finite when the language is nonregular.
Question No: 5 ( Marks: 1 ) - Please choose one
A regular
language:
*► Must be finite
► Must be infinite
► Can be finite or infinite
► Must be finite and cannot be infinite
Question No: 6 ( Marks: 1 ) - Please choose one
Every
regular expression can be expressed as CFG but every CFG cannot be expressed as a
regular expression.
This statement is:
► Depends on the language
► None of the given options
*► True
► False
Question No: 7 ( Marks: 1 ) - Please choose one
ab
a
X1–
b
X2+
Above given FA corresponds RE r. then FA corresponding to r* will be
a
b
b
z3+
a
z2
z1±
ba
This statement is
*► True
► False
► Depends on language
► None of these
Question No: 8 ( Marks: 1 ) http://vustudents.ning.com- Please choose one
Consider
the language L of strings, defined over Σ = {a,b}, ending in a
► There are finite many classes generated by L, so L is regular
*► There are infinite many classes generated by L, so L is regular
► There are finite many classes generated by L, so L is non-regular
► There are infinite many classes generated by L, so L is non-regular
Question No: 9 ( Marks: 1 ) - Please choose one
ab,ba
ab,ba
±
aa,bb aa,bb
Above given TG has _____________ RE.
► (aa+aa+(ab+ab)(aa+ab)*(ab+ba))*
*► (aa+bb+(ab+ba)(aa+bb)*(ab+ba))*
► (aa+bb+(ab+ba)(aa+bb)(ab+ba))*
► None of these
Question No: 10 ( Marks: 1 ) - Please choose one
The word
‘formal’ in formal languages means
*► The symbols used have well defined meaning
► They are unnecessary, in reality
► Only the form of the string of symbols is significant
► None of these
Question No: 11 ( Marks: 1 ) - Please choose one
Let A = {0,
1}. The number of possible strings of length ‘n’ that can be formed by the elements of the
set A is
http://vustudents.ning.com
► n!
*► n2
► nm
► 2n
Question No: 12 ( Marks: 1 ) - Please choose one
Choose the
correct statement.
► A Mealy machine generates no language as such
► A Moore machine generates no language as such
*► A Mealy machine has no terminal state
► All of these
Question No: 13 ( Marks: 1 ) - Please choose one
TM is more
powerful than FSM because
► The tape movement is confined to one direction
*► It has no finite state control
► It has the capability to remember arbitrary long sequences of input symbols
► None of these
Question No: 14 ( Marks: 1 ) - Please choose one
If L1 and
L2 are expressed by regular expressions r1 and r2, respectively then the language
expressed by r1 + r2
will be _________
* ► Regular
► Ir-regular
► Can’t be decided
► Another Language which is not listed here
Question No: 15 ( Marks: 1 ) - Please choose one
Like TG, a
PDA can also be non-deterministic
► True
*► False
Question No: 16 ( Marks: 1 ) - Please choose one
The above machine is a/anTG ___________ http://vustudents.ning.com
► Finite Automata
*► Turing machine
► FA
► TG
Question No: 17 ( Marks: 1 ) - Please choose one
The
language of all words (made up of a’s and b’s) with at least two a’s can not be described
by the regular
expression.
► a(a+b)*a(a+b)*(a+b)*ab*
► (a+b)* ab* a(a+b)*
► b*ab* a(a+b)*
► none of these
Question No: 18 ( Marks: 1 ) - Please choose one
In FA, if
one enters in a specific state but there is no way to leave it, then that specific state is
called
*► Dead State
► Waste Basket
► Davey John Locker
► All of these
Question No: 19 ( Marks: 1 ) - Please choose one
If L is a
regular language then, Lc is also a _____ language.
*► Regular
► Non-regular
► Regular but finite
► None of the given
Question No: 20 ( Marks: 1 ) - Please choose one
In CFG, the
symbols that can’t be replaced by anything are called___
► Terminal
► Non-Terminal
*► Production
► All of given
Question No: 21 ( Marks: 1 ) - Please choose one
Which of
the following is NOT a regular language? http://vustudents.ning.com
► String of 0’s whose length is a perfect squere
*► Set of all palindromes made up of 0’s and 1’s
► String of 0’s whose length is a prime number
► All of the given options
Question No: 22 ( Marks: 1 ) - Please choose one
Choose the
incorrect (FALSE) statement.
► A Mealy machine generates no language as such
► A Mealy machine has no terminal state
*► For a given input string, length of the output string generated by a Moore machine is
not more than the length of the output string generated by that of a Mealy machine
► All of these
Question No: 23 ( Marks: 1 ) - Please choose one
Pumping
lemma is generally used to prove that:
► A given language is infinite
*► A given language is not regular
► Whether two given regular expressions of a regular language are equivalent or not
► None of these
Question No: 24 ( Marks: 1 ) - Please choose one
Which of
the following is a regular language?
► String of odd number of zeroes
► Set of all palindromes made up of 0’s and 1’s
*► String of 0’s whose length is a prime number
► All of these
Question No: 25 ( Marks: 1 ) - Please choose one
Choose the
incorrect statement:
► (a+b)*aa(a+b)* generates Regular language.
► A language consisting of all strings over Σ={a,b} having equal number of a’s and b’s
is a
regular language
► Every language that can be expressed by FA can also be expressed by RE
► None of these
Question No: 26 ( Marks: 1 ) - Please choose one
Left hand
side of a production in CFG consists of:
► One terminal
► More than one terminal
► One non-terminal
* ► Terminals and non-terminals
Question No: 27 ( Marks: 2 )
Diffrentiate
between Regular and Non regular languages?
Ans:
The main difference between regular and non regular language are as:
1. The regular language is that language which can be expressed by RE is known as
regular language
whereas any language which can not be expressed by RE is known as non regular
language.
Question No: 28 http://vustudents.ning.com ( Marks: 2 )
What is
meant by a "Transition" in FA?
Question No: 29 ( Marks: 2 )
What are
the halt states of PDAs?
Ans:
There are some halts states in PDA which are as:
1. Accept or reject stat is also halt state.
2. Reject state is like dead non final state.
3. Accept state is like final state.
Question No: 30 ( Marks: 2 )
Identify the
null productions and nullable productions from the following CFG:
S -> ABAB
A -> a | /\
B-> b | /\
Question No: 31 ( Marks: 3 )
Describe
the POP operation and draw symbol for POP state in context of Push down stack.
Question No: 32 ( Marks: 3 )
What does
the the following tape of turing machine show?
READ9 READ3 b b abb 11
ROW
Number
PUSH
What
POP
What
READ
What
TO
Where
FROM
Where
Ans:
Arbitrary Summary Table:
The arbitrary summary table shows the trip from READ9 to READ3 does not pop one
letter form the STACK it adds two letters to the STACK.
Row11 can be concatenated with some other net style sentences e.g. row11 net(READ3,
READ7,
a)Net(READ7, READ1, b)Net(READ1, READ8, b) it gives the non terminal
Net(READ9, READ8, b),
The whole process can be written as:
Net(READ9, READ8, b) ?Row11Net(READ3, READ7,a) Net(READ7, READ1,
b)Net(READ1,
READ8, b)
This will be a production in the CFG of the corresponding row language.
Question No: 33 ( Marks: 3 )
Find Pref
(Q in R) for:
Q = {10, 11, 00, 010}
R = {01001, 10010, 0110, 10101, 01100, 001010}
Question No: 34 ( Marks: 5 )
Consider
the Context Free Grammar (CFG)
S à 0AS | 0
A à S1A | SS | 1a
Show that the word 0000100 can be generated by this CFG by showing the whole
derivation
starting from S
Question No: 35 ( Marks: 5 )
Consider
the language L which is EVEN-EVEN, defined over Σ = {a,b}. In how many classes does
L may
partition Σ*. Explain briefly.
Question No: 36 ( Marks: 5 )
What are
the conditions (any five) that must be met to know that PDA is in conversion form?
http://vustudents.ning.com
Ans:
Conversion form of PDA:
A PDA is in conversion form if it has following conditions:
1. The PDA must begin with the sequence
2. There is only one ACCEPT state.
3. Every edge leading out of any READ or HERE state goes directly into a POP state.
4. There are no REJECT states.
5. All branching, deterministic or nondeterministic occurs at READ or HERE states.
6. The STACK is never popped beneath this $ symbol.
7. No two POPs exist in a row on the same path without a READ or HERE.
8. Right before entering ACCEPT this symbol is popped out and left.
1.What is Row Langage.
2.What does FA stands for?
3.What are live and dead productions.
4. Given a summary table, we were required to explain it.
5.What do you mean by wanted and unwanted branches.
6.Given an FA, I had to recogize the langauge - EVEN-EVEN
7.Given the CFG, had to write the language (EQUAL)
8.Construct corresponding CFG for the given language
(1) All words of even length but not multiple of 3.
(2) Palindrome (both even and odd palindrome). (5 mark)
9.Who invented Turing m/c
10.Equivalent /non-equivalent langages
11. what are formal langages?
Q No. 1
Choose the right option: (2)
A) aAbB is a string defined on an alphabet {aA, bB, aAbB}.
B) aAbB is a string defined on an
alphabet {aA, bB}.
o B only
o A only
Q No. 2
Choose the right option: (2)
A) For every NFA, there may not be an FA equivalent to it
B) For every NFA, there must be an
FA equivalent to it
o B only
o A only
Q No. 3
Choose the right option: (2)
A) In a Mealy machine, the set of letters and the set of output
characters must be
same
B) In a Mealy machine, the set of letters and the set of output
characters may not be
same
o B only
o A only
Q No. 4
Choose the right option: (2)
A) Pumping Lemma version I is sufficient to test an infinite language to be
regular
B) To test an infinite language to be regular, Pumping Lemma
version I may not help
o B only
o A only
Q No. 5
Choose the right option: (2)
A) For a given CFG, there may not exist any PDA accepting the
language generated by
the CFG
B) For a given CFG, there must be a PDA accepting the language
generated by the
CFG
o B only
o A only
Q No. 6
Identify the language accepted by the following PDA. Build an
FA accepting the corresponding language. Write the
corresponding RE as well (10)
Q No. 7
Derive any two words of length 4 from the
following CFG. (5) S®XaaX, X®aX|bX|L
A Total Language Tree has
o
o
o
All languages over
All strings over
Σ
Σ
All words of all languages over
Σ
Σ
o
All words of one language over
Question No. 2
(a) Derive any two words of length 4 from the following CFG.
S→XaaX, X→aX|bX|�.
Write the corresponding RE as Well.
(b) Determine the CFG, corresponding to the following FA
ab
b
a
S- b
b
Question No. 3
What Turing Machine does not have?
o Stack
o
o
o
Tape
Head
Word
Question No. 4
A
a
a
B
b
(a) Draw Moore Machine equivalent to following Mealy Machine. (5)
q1 1/1
1/0
0/0
q0 0/1 q3 1/0
0/0 1/0
q2
0/1
(b) Use Pumping Lemma II to show that following language is non-regular.
n2
(5)
i. Square ( a , for n = 1, 2, 3, ….)
Question No. 5
M
arks : 10
Identify the language accepted by the following PDA. Build an FA accepting the
corresponding language. Write the corresponding RE as well.
Question No. 6
M
arks : 02
Two FAs represent same languages over some alphabet (may or may not be same
for
FAs), If
o They accept same words
o
o
o
They accept same number of words
o
o
o
aab*
They reject same words
None of above
Question No. 7
M
arks : 02
CFG given S � bS|Sb|aa represents language
o b*aa
b*aab*
b*(aa)*b*
Question No. 8
M
arks : 10
a) Define the following terms
(6)
i. Total language tree (TLT)
ii. Ambiguous CFG.
iii. Unit Production
(b) Find Context Free Grammar's (CFG's) for the following languages over the Σ={a, b}.
(4)
i. All the words that do not contain substring abb.
ii. All the words that have exactly two or three b's.
Question No. 9
M
arks : 02
A Language that is finite but not regular
o Λ
o
o
o
(a+b)*
Φ
All strings of a's in Σ = {a,.b}
Question No. 1 Marks :
A production of the form non-terminal � non-terminal is called a dead Production.
1. True
2. False
Question No. 2
Marks : 3
Semi-word is a string having some terminals and one non-terminal at the right of
string.
1. True
2. False
Question No. 3
Marks : 3
Two FAs are equivalent if they have same no. of states.
1. True
2. False
Question No. 4
Marks : 1
There exist exactly two different derivations in an ambiguous CFG for a word.
1. True
2. False
Question No. 5 Marks :
Construct RE’s for following languages over Σ= {a, b}
i. All words which contain substring “baba”. [5]
ii.A ll words which never end in substrings “aa” and “ab” [5]
Question No. 6
Marks : 1
Regular languages are closed under Union, Concatenation and Kleene star.
1. True
2. False
Question No. 7
Marks : 1
C FG may also represent a regular language.
1. True
2. False
Question No. 8
Marks : 1
Find the complement of the FA below,
Question No. 9
Marks : 1
PDA is stronger than FA.
3. True
4. False
Question No. 10 Marks : 3
Union of two FAs is an FA that accepts all the string of FA1 and FA2.
True
False
Question No. 11 Marks :
Given a CFG below,
a) Remove Unit productions from the CFG. [5]
S→S+T|T
T→T*F|F
F→(S)|a
b) Derive CNF corresponding to the CFG given below. [10]
S → ABa
A → aab
B → Ac
Question No. 12 Marks :
In non-deterministic PDA a string may be traced by more than one paths.
1. True
2. False
Question No. 13 Marks :
There always exist an FA for each PDA.
True
False
Question No. 14 Marks :
a) Given an FA below, [5]
What is language accepted by above FA?
b) Draw a non-deterministic PDA for the above FA. [10]
Question No: 1 ( Marks: 1 ) - Please choose one
PDA is only used to represent a regular language.
► True
► False
Question No: 2 ( Marks: 1 ) - Please choose one
If L is a regular language then LC is also a regular language.
► True
► False
Question No: 3 ( Marks: 1 ) - Please choose one
A production of the form non-terminal � string of two non-terminal is called a live
Production.
► True
► False
Question No: 4 ( Marks: 1 ) - Please choose one
we can find a CFG corresponding to a DFA.
► True
► False
Question No: 5 ( Marks: 1 ) - Please choose one
START, READ, HERE and ACCEPTS are conversions of the machine
► True
► False
Question No: 6 ( Marks: 1 ) - Please choose one
A CFG is said to be ambiguous if there exists at least one word of its language that
can
be generated by different production trees
► True
► False
Question No: 7 ( Marks: 1 ) - Please choose one
Syntax tree or Generation tree or Derivation tree are same tree
► True
► False
Question No: 8 ( Marks: 1 ) - Please choose one
The symbols that cannot be replaced by anything are called terminals
► True
► False
Question No: 9 ( Marks: 1 ) - Please choose one
The production of the form non-terminal � one non-terminal is called unit
production
► True
► False
Question No: 10 ( Marks: 1 ) - Please choose one
DFA and PDA are equal in power.
► True
► False
Question No: 11 ( Marks: 10 )
a) Define Describe the following terms:
[Note: maximum in 20 to 30 words for each]
I. CNF
II. Regular Grammar
b) Convert the following CFG into CNF
S → CDCD
C → 0|Λ
D → 1|Λ
Question No: 12 ( Marks: 10 )
a) Construct RE’s for following languages over Σ= {0, 1} (6)
i. All words in which “1” never follows “0”. ( “0” never appears before
“1”)
ii. All words which begin and end with different letters.
b) How many minimum states can be there in an NFA of language
having all word
with “101” at the end? (4)
HINT: Build NFA for language for yourself but write only number of
minimum states. No need to build NFA in software.
Question No: 13 ( Marks: 10 )
a) Is this an FA or NFA? (2)
b) Determine the CFG corresponding to the above FA or NFA (8)
Question No: 14 ( Marks: 10 )
a) Given CFG (Context Free Grammar): (6)
S → bS | aX | Λ
X → aX | bY | Λ
Y → aX | Λ
Derive following strings from above CFG. Show all steps. If string
cannot be derived then describe it.
i. baabab
ii. ababaab
b) Describe language of following PDA (Push Down Automata): (4)
[ Note: Don’t write more than two to three lines for each. Only write to the point. ]
START
0
READ
ACCEPT
Question No: 15
1
1
( Marks: 5 )
Given a CFG below, [5]
S → bS | aM
M→ bM | aF
F → bF | aM | ^
What is language accepted by above CFG?
Question No: 1 ( Marks: 1 ) - Please choose one
a* + b* = (a + b)* this expression is __________
True
False
Can t be decided
None of these
Question No: 2 ( Marks: 1 ) - Please choose one
a (a + b)* is the RE of language defined over
True
False
Such a language does not exist
None of these
= {a, b} ha
Question No: 3 ( Marks: 1 ) - Please choose one
According to _________ machine, Finite set of states containing
exactly one START state and
some (may be none) HALT states that cause execution to terminate
when the HALT states are
entered.
Finite Automata
TG
Turing
Insertion
Question No: 4 ( Marks: 1 ) - Please choose one
finite automaton but with an unlimited and unrestricted
memory
A Turing machine is a much more accurate model of a general purpose
computer
Both satements are false
Both statments are true.
Question No: 8 ( Marks: 1 ) - Please choose one
To determine whether a string is generated by the given CFG
CYK algorithm is used
CIK algorithm is used
CNK algorithm is used
CNM algorithm is used
Question No: 9 ( Marks: 1 ) - Please choose one
The process of finding the derivation of word generated by particular grammar is called_____
Processing
Parsing
Programming
Planing
Question No: 10 ( Marks: 1 ) - Please choose one
Pumping Lemma II says that length(x) + length(y) should be
Less than number of states
Less than or equal to number of states
Greater than number of states
Greater than or equal to number of states
Question No: 11 ( Marks: 1 ) - Please choose one
Before the PDA is converted into conversion form a new
state _____ is defined which is placed in the middle of any
edge.
, L1 L2
None of the given
Question No: 15 ( Marks: 1 ) - Please choose one
If L is a regular language then, Lc is also a _____ language.
Regular
Non-regular
Regular but finite
None of the given
Question No: 16 ( Marks: 1 ) - Please choose one
Running the string abbabbba on this Moore
machine. The outputs will be________
q1/0
aa
q0/1
b
b
b
101111010
01111010
01011110
01010101
Question No: 17
a
b q2/1
b
a
1
a
q3/0 2
( Marks: 1
a
aa
a
b
b
a
b
b
ab
ba
ba
a
a
bb
bb
Above given FA has ___________ final states
1
2
3
+
Above given FA s are ___________
Non-equivalent
FA2 is not valid as it
has no final state.
None of these
Equivalent
Question No: 19 ( Marks: 1 ) - Please choose one
2a4
a
a b a,b
1 a b 6+
bab
3b5
RE for the above given FA is __________________.
(a+b)* (aaa + bbb) (a+b)* OR (a+b)* (aaa) (a+b)* + (a+b)*(bbb) (a+b)*
(a+b)* (aaa + bbb) (a+b)*
(a+b)* (aaa) (a+b)* +
(a+b)*(bbb) (a+b)*
(a+b)* (aaa + bbb)*
(a+b)*
Question No: 20 ( Marks: 1 ) - Please choose one
One FA has n states and m letters in the alphabet. Then FA will have _____
number of states in the diagram.
(m)(n)
(n)(m)
(m)(n) & (n)(m)
None of these
Question No: 21 ( Marks: 1 ) - Please choose one
Choose the incorrect statement.
For a given input string, length of the output strings generated by a Moore
machine is not more than the length of the output strings generated
by that of a Mealy machine
A Mealy machine generates no language as such
All of these
A Mealy machine has no terminal state
Question No: 22 ( Marks: 1 ) - Please choose one
Pumping lemma is generally used for proving
A given grammar is regular
A given grammar is not regular
Whether two given regular expressions are equivalent
None of these
Question No: 23 ( Marks: 1 ) - Please choose one
Which of the following pairs of regular expressions are not equivalent?
(ab)* and a*b*
x(xx)* and (xx)*x
x+ and x*x+
All of these
Question No: 24 ( Marks: 1 ) - Please choose one
Choose the correct statements.
A = {an bn | n = 0, 1, 2, 3, } is a regular language.
The set of B, consisting of all strings made up of only a s
and b s having equal number of a s and b s defines a regular
language
L(A*B*) B gives the set of A
None of these
Question No: 25 ( Marks: 1 ) - Please choose one
Choose the incorrect statements.
A = {an bn | n = 0, 1, 2, 3, } is a regular language
The set of B, consisting of all strings made up of only a s
and b s having equal number of a s and b s defines a regular
language
L(A*B*) B gives the set of A
None of these
Question No: 26 ( Marks: 1 ) - Please choose one
The logic of pumping lemma is a good example of
The divide and conquer technique
Recursion
Iteration
The Pigeon-hole principal
Question No: 27 ( Marks: 1 ) - Please choose one
Palindrome can be recognized by FSM because
An FSM can t remember arbitrarily large
amount of information An FSM can t
deterministically fix the mid-point
Even if the mid-point is known, an FSM can t find whether the
second half of the string matches the first half
None of these
Question No: 28 ( Marks: 1 ) - Please choose one
The language all words (made up of a s and b s) with at least two a s can be described by
the regular expression.
(a+b)* a (a+b)* a (a+b)*
(a+b)* ab* a(a+b)*
b*ab* a(a+b)*
All of these
Question No: 29 ( Marks: 1 ) - Please choose one
The language all words (made up of a s and b s) with at least two a s can not be
described by the regular expression.
a(a+b)*a(a+b)*(a+b)*ab*
(a+b)* ab* a(a+b)*
b*ab* a(a+b)*
none of these
Question No: 30 ( Marks: 1 ) - Please choose one
An alphabet of is valid if
No letter of appears in middle
of any other letter No letter of
appears at end of any other
letter
No letter of appears at start of
any other letter
All of above
Question No: 31 ( Marks: 1 )
Can you neglect the following?
Pumping lemma is generally used for proving that a given grammar is regular.
Question No: 32 ( Marks: 1 )
Is it correct that the regular expression can not be used for simulating sequential
circuits?
Question No: 33 ( Marks: 2 )
Differentiate between containing and consisting?
Question No: 34 ( Marks: 2 )
How can you determine that any two FAs can generate the equivalint
language?
Question No: 36 ( Marks: 3 )
Find Pref (Q in R) for:
Q = {01, 10, 11, 011}
R = {10011, 100100, 01010, 0111, 010100, 01011}
Question No: 37 ( Marks: 3 )
What are the Joints of PDA?
Question No: 38 ( Marks: 5 )
Consider the Context Free Grammar (CFG)
S aAS | a
A SbA | SS | ba
Show that the word aaaabaa can be generated by this CFG by
showing the whole derivation starting from S
Question No: 39 ( Marks: 5 )
Construct RE for following languages over = {a, b}
All words containing exactly 4 a (mean, there must be 4 a neither less nor
extra)
Question No: 40 ( Marks: 10 )
Decide whether or not the word babab is generated by the
following grammar using CYK algorithm. Show all steps.
S AB | CD | a | b
Aa
B SA
C DS
Db
Question No: 41 ( Marks: 10 )
Explain the Emptiness Algorithm?
Question No: 1 ( Marks: 1 ) - Please choose one
(a+b)*a(a+b)*b(a+b)* is the RE of language defined over
and one b={a,b} having at least one a ={a,b} having at least one a
True
False
Such a language does not exist
None of these
Question No: 2 ( Marks: 1 ) - Please choose one
If r1 = (aa + bb) and r2 = ( a + b) then the language (a + b)* (aa + bb)* will be
generated by
(r2)(r1)
(r1 + r2)*
(r2)*(r1)*
(r1)*
Question No: 3 ( Marks: 1 ) - Please choose one
In FA starting state is represented by a ________ sign.
+
*
S
Question No: 4 ( Marks: 1 ) - Please choose one
Who did not invent the Turing machine?
Alan Turing
A. M. Turing
Turing
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
According to _________ machine, Finite set of states containing exactly
one START state and
some (may be none) HALT states that cause execution to terminate
when the HALT states are
entered.
Finite Automata
TG
Turing
Insertion
Question No: 6 ( Marks: 1 ) - Please choose one
Can a turing machine's head ever be in the same location in two successive
steps?
Yes
Yes but only in finite languages
No
Yes but only in infinite langauges
Question No: 7 ( Marks: 1 ) - Please choose one
Examin the following CFG and
select the correct choice S
AB, A BSB, B CC
C SS
A a|b
C b|bb
abb is a word in the corresponding CFL.
abb is not the word of corresponding CFL.
any word can be accept from the corresponding CFL.
Non of these
Question No: 8 ( Marks: 1 ) - Please choose one
To determine whether a string is generated by the given CFG
CYK algorithm is used
CIK algorithm is used
CNK algorithm is used
CNM algorithm is used
Question No: 9 ( Marks: 1 ) - Please choose one
The process of finding the derivation of word generated by particular grammar is called_____
Processing
Parsing
Programming
Planing
Question No: 10 ( Marks: 1 ) - Please choose one
Converting the given CFG in CNF is the first rule of _____
CYK algorithm
CKY algorithm
KYC algorithm
CNK algorithm
Question No: 11 ( Marks: 1 ) - Please choose one
Which statement is true?
The PDA must have one accept state
and one reject state The PDA must
have one accept state and two reject
state The PDA must have two accept
state and two reject state There is no
reject state in the PDA.
Question No: 12 ( Marks: 1 ) - Please choose one
If a language can be expressed by a regular expression,
then its complement cannot be expressed by a regular
expression. This statement is:
True
False
Depends on language
None of the given optios
Question No: 13 ( Marks: 1 ) - Please choose one
Left hand side of CFG may consist of:
One terminal
More than one terminal
One non-terminal
Terminals and non-terminals
Question No: 14 ( Marks: 1 ) - Please choose one
Choose the correct answer?
The set of input letters and the set of output characters in a Moore
machine, may not be same
The set of input letters and the set of output characters in a Moore
machine, must be same.
Question No: 15 ( Marks: 1 ) - Please choose one
The symbols that can t be replaced by anything are called___
Terminal
Non-Terminal
Production
All of given
Question No: 16 ( Marks: 1 ) - Please choose one
+
b(a+b)*a
a( a+b)* b
+
Above given GTG accepts the language in which strings
Begins and ends with different letters
Begins and ends with same letters
Have length greater than 1
None of these
Question No: 17 ( Marks: 1 ) - Please choose one
If L1 and L2 are two regular languages, then ______ is also regular.
L1 L2
L1 L2
Both L1 L2 , L1 L2
None of the given
Question No: 18 ( Marks: 1 ) - Please choose one
If L is a regular language then, Lc is also a _____ language.
Regular
Non-regular
Regular but finite
None of the given
Question No: 19 ( Marks: 1 ) - Please choose one
a, b
-b1^ +
Above given structure is a ______________
FA
NFA
NFA - ^
None of these
Question No: 20 ( Marks: 1 ) - Please choose one
a, b
2 b 4+
a
1- a,b
b
3 a 5+
Above given TG represents the language____
Begins and ends with same letters
Begins and ends
with different
letters Begins with
a
None of these
Question No: 21 ( Marks: 1 ) - Please choose one
A language can be defined through Transition Graph.
False
True
Depends on alphabet
None of these
Question No: 22 ( Marks: 1 ) - Please choose one
The word formal in formal languages means
The symbols used have well defined meaning
They are unnecessary, in reality
Only the form of the string of symbols is significant
None of these
Question No: 23 ( Marks: 1 ) - Please choose one
Pumping lemma is generally used for proving
A given grammar is regular
A given grammar is not regular
Whether two given regular expressions are equivalent
None of these
Question No: 24 ( Marks: 1 ) - Please choose one
Choose the incorrect statements.
A = {an bn | n = 0, 1, 2, 3, } is a regular language
The set of B, consisting of all strings made up of only a s
and b s having equal number of a s and b s defines a regular
language
L(A*B*) B gives the set of A
None of these
Question No: 25 ( Marks: 1 ) - Please choose one
The logic of pumping lemma is a good example of
The divide and conquer technique
Recursion
Iteration
The Pigeon-hole principal
Question No: 26 ( Marks: 1 ) - Please choose one
Palindrome can t be recognized by FSM because.
An FSM can t remember arbitrarily large amount of information.
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An FSM can t deterministically fix the mid-point
Even if the mid-point is known, an FSM can t find whether the
second half of the string matches the first half
All of these
Question No: 27 ( Marks: 1 ) - Please choose one
Palindrome can be recognized by FSM because
An FSM can t remember arbitrarily large
amount of information An FSM can t
deterministically fix the mid-point
Even if the mid-point is known, an FSM can t find whether the
second half of the string matches the first half
None of these
Question No: 28 ( Marks: 1 ) - Please choose one
The FSM in the following picture is a.
Mealy machine
Moore machine
Kleene machine
None of these
Question No: 29 ( Marks: 1 ) - Please choose one
Following machine is.
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complement a given bit pattern
generates all strings of 0 s and 1 s
adds 1 to a given bit pattern
none of these
Question No: 30 ( Marks: 1 ) - Please choose one
The language all words (made up of a s and b s) with at least two a s can not be
described by the regular expression.
a(a+b)*a(a+b)*(a+b)*ab*
(a+b)* ab* a(a+b)*
b*ab* a(a+b)*
none of these
Question No: 31 ( Marks: 1 )
Is the following pairs of regular
expressions are equivalent? x+ and x*x+
Question No: 32 ( Marks: 1 )
Can you neglect that the any given Moore machine has an equivalent Mealy machine?
Question No: 33 ( Marks: 2 )
What is Lexical Analyzer?
Question No: 34 ( Marks: 2 )
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Why we use null string in FA?
Question No: 35 ( Marks: 3 )
Find Pref (Q in R) for:
Q = {01, 10, 11, 011}
R = {10011, 100100, 01010, 0111, 010100, 01011}
Question No: 36 ( Marks: 3 )
What does mean the LANGUAGE IS CLOSED?
Question No: 37 ( Marks: 3 )
How to differentiate between "wanted" and "unwanted branch"?
Question No: 38 ( Marks: 5 )
Give Regular Expressions (REs) for the following languages.
i) Let = {a, b, c}; all words that contain at least one double letter in them.
ii) Let = {a, b}; having even numbers of a s and even number of b s
Note: Helpful symbol(s):
Question No: 39 ( Marks: 5 )
Decide whether or not the following grammer generates
any words using Emptyness algorithm discussed in the
lectures. Show all steps.
S AB
A SB | a
B SA | b
Question No: 40 ( Marks: 10 )
Find DFA for the following CFG
S bS | aY
Y aY | bZ
Z aY | bS | ^
Question No: 41 ( Marks: 10 )
Question No: 1 ( Marks: 1 ) - Please choose one
To access the element of two dimensional array we use,
► Single referencing
► Single dereferencing
► Double dereferencing
► Double referencing
Question No: 2 ( Marks: 1 ) - Please choose one
setprecision is a parameter less manipulator.
► True
► False
Question No: 3 ( Marks: 1 ) - Please choose one
Which of the following is NOT a preprocessor directive?
► #error
► #define
► #line
► #ndefine
Question No: 4 ( Marks: 1 ) - Please choose one
We can use New keyword inside of Class Constructor.
► True
► False
Question No: 5 ( Marks: 1 ) - Please choose one
It is possible to return an object from a function through this pointer.
► True
► False
Question No: 6 ( Marks: 1 ) - Please choose one
We can change the artiy (Number of operands required) of an operator through operator
overloading
► True
► False
Question No: 7 ( Marks: 1 ) - Please choose one
new and delete operators cannot be overloaded.
► True
► False
Question No: 8 ( Marks: 1 ) - Please choose one
The statement cin.get (); is used to,
► Read a string from keyboard
► Read a character from keyboard
► Read a string from file
► Read a character from file
Question No: 9 ( Marks: 1 ) - Please choose one
When an array of object is created dynamically then there is no way to provide parameterized
constructors for array of objects.
► True
► False
Question No: 10 ( Marks: 1 ) - Please choose one
We can delete an array of objects without specifying [] brackets if a class is not doing
dynamic
memory allocation internally.
► True
► False
Question No: 11 ( Marks: 1 ) - Please choose one
The insertion (<<) and extraction (>>) operators are unary operators.
► True
► False
Question No: 12 ( Marks: 1 ) - Please choose one
What will be the correct syntax for the following function call?
float square (int &);
► square (int num);
► square (&num);
► square (num);
► square (*num);
Question No: 13 ( Marks: 1 ) - Please choose one
What will be the output of the following code segment?
char *x = ”programming” ;
cout << *(x+2) << *(x+3) << *(x+5) << *(x+8) ;
► ogai
► ramg
► prgm
► rorm
Question No: 14 ( Marks: 1 ) - Please choose one
When an operator function is define as member function then operand on the left side of
operator
must be an object.
► True
► False
Question No: 15 ( Marks: 1 ) - Please choose one
Increment and decrement operators are ______.
► Binary operators
► Unary operators
► Logical operators
► Conditional operators
Question No: 16 ( Marks: 1 ) - Please choose one
UNIX has been developed in ________ language.
► JAVA
►B
►C
► FORTRAN
Question No: 17 ( Marks: 1 ) - Please choose one
Which of the following is used with bit manipulation?
► Signed integer
► Un-signed integer
► Signed double
► Un-signed double
Question No: 18 ( Marks: 1 ) - Please choose one
We want to access array in random order which approach is better?
► Pointers
► Array index
► Both pointers and array index are better
► None of the given options.
Question No: 19 ( Marks: 1 ) - Please choose one
Which of the following is the correct C++ syntax to allocate space dynamically for an array
of 10
int?
► new int(10) ;
► new int[10] ;
► int new(10) ;
► int new[10];
Question No: 20 ( Marks: 1 ) - Please choose one
Which of the following will be the correct function call for function prototype given below?
int func (int &);
► func(int num);
► func(&num);
► func(num);
► func(*num);
Question No: 21 ( Marks: 1 ) - Please choose one
For non-member operator function, object on left side of the operator may be
► Object of operator class
► Object of different class
► Built-in data type
► All of the given options
Question No: 22 ( Marks: 1 ) - Please choose one
Which of the following object(s) will call the member operator function within the statement
given
below?
obj1=obj2+obj3;
► Object obj1
► Object obj2
► Object obj3
► Any of the object
Question No: 23 ( Marks: 1 ) - Please choose one
The static data members of a class will be ________
► shared by objects
► created for each object
► initialized within class
► initialized within main function
Question No: 24 ( Marks: 1 ) - Please choose one
Which of the following is used for allocating space for static variables?
► Heap
► Static storage area
► Free store
► Stack
Question No: 25 ( Marks: 1 ) - Please choose one
The default value of a parameter can be provided inside the ________________
► function prototype
► function definition
► both function prototype or function definition
► none of the given options.
Question No: 26 ( Marks: 1 ) - Please choose one
Initializing the data members in the definition of the class is ___________
► syntax error
► logical error
► not an error
► none of the given options
Question No: 27 ( Marks: 1 ) - Please choose one
It is possible to define a class within another class.
► True
► False
Question No: 28 ( Marks: 1 ) - Please choose one
A template function must have
► One or more than one arguments
► Only one argument
► Zero arguments
► None of the given options
Question No: 29 ( Marks: 1 ) - Please choose one
Where we can include a header file in the program?
► any where
► in start
► at the end
► none of the given options.
Question No: 30 ( Marks: 1 ) - Please choose one
Truth tables are used for analyzing ___________.
► logical expressions
► arithmetic expressions
► both logical and arithmetic expressions
► none of the given options.
True or False
1. In a finite language no string is pumpable. True
2. A DFA has infinite number of states. False
3. A DFA can have more than one accepting state. True
4. In DFA all states have same number of transitions. True
5. Every subset of a regular language is regular. False
6. Let L4 = L1L2L3. If L1 and L2 are regular and L3 is not regular, it is possible that L4 is
regular. True
7. In a finite language no string is pumpable. True
8. If A is a nonregular language, then A must be infinite. True
9. Every context-free language has a context-free grammarin Chomsky normal form. True
10. If A is a context-free language, then A must be nonregular. False
11. The class of regular languages is closed under intersection. True
12. If a language A is regular, then it A must be finite. False
13. Every language is Turing-recognizable. False
14. If a language is context-free, then it must be Turing-decidable. True
15. The problem of determining if a context-free grammar generates
the empty language is undecidable. False
16. The problem of determining if a Turing machine recognizes the
empty language is undecidable. True
17. The set of all languages over an alphabet is countable.False
18. There are some languages recognized by a 5-tape, nondeterministic
Turing machine that cannot be recognized by a 1-tape,
deterministic Turing machine.False
19. The language { 0n1n | 0 ≤ n ≤ 1000 } is regular. True
20. Nonregular languages are recognized by NFAs. False
21. The class of context-free languages is closed under intersection. False
22. A language has a regular expression if and only if it
has an NFA. True
23. The regular expression (01*0 ∪ 1)*0 generates the language
consisting of all strings over {0, 1} having
an odd number of 0’s. False
24. If a language A has a PDA, then A is generated by a
context-free grammar in Chomsky normal form. True
25. If A is a context-free language and B is a language such that B is a subset of A, then B
must
be a context-free language. False
26. If a language A has an NFA, then A is nonregular. False
27. The regular expressions (a ∪ b)* and (b*a*)* generate the same language. True
28. If a language A has a regular expression, then it also has a context-free grammar. True
Regular Expressions
Describe the language denoted by the following regular expressions:
a) a(a|b)*a
The expression denotes the set of all strings of length two or more that start and end with an
‘a’.
b) ((e|a)b*)*
The expression denotes the set of all strings over the alphabet {a,b}.
c) (a|b)*a(a|b)(a|b)
The expression denotes the set of all strings of length 3 or more with an ‘a’ in the third
position from
the right. Ie of form yaxz where y is an arbitrary string , and x and z are single characters.
d) a*ba*ba*ba*
The expression denotes the set of all strings that contain precisely 3 b’s.
e) (aa|bb)*((ab|ba)(aa|bb)*(ab|ba)(aa|bb)*)*
The expression denotes the set of all strings of even length.
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start state by
the
transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b. (ba+a)* c.
a*(aa*b)* d. (a*b*)*
a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*.
{ x}*, { x}+, {a+b}*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must correspond
to the
initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Question # 4 of 10 ( Start time: 11:16:41 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Question # 5 of 10 ( Start time: 11:17:26 PM ) Total Marks: 1
If S = {aa, bb}, then S* will not contain
Aabbaa
Bbaabbbb
Aaabbb
aabbaaaa
Question # 6 of 10 ( Start time: 11:18:55 PM ) Total Marks: 1
Formal is also known as _________
Syntactic language
Semantic language
Informal language
None of these
Question # 7 of 10 ( Start time: 11:20:15 PM ) Total Marks: 1
In an FA, when there is no path starting from initial state and ending in final state then that FA
accept null string
accept all strings
accept all non empty strings
does not accept any string
Question # 9 of 10 ( Start time: 11:22:33 PM ) Total Marks: 1
FA of EVEN language shows null string when
Initial state is final as well
EVEN does not accept null
One state is declared null
None of the these
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start state by
the
transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b. (ba+a)* c.
a*(aa*b)* d. (a*b*)*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must correspond
to the
initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 ( Start time: 05:55:36 PM ) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Quiz Start Time: 06:37 AM
Time Left 19
sec(s)
Question # 1 of 10 ( Start time: 06:37:52 AM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one final state then
Select correct option:
Introduce the new final state
Eliminate the old final state
Replace the old final state with start state
Replace the old final state with new start state
Quiz Start Time: 06:37 AM
Time Left 60
sec(s)
Question # 2 of 10 ( Start time: 06:39:16 AM ) Total Marks: 1
If two RE’s generate same language then these RE’s are called
Select correct option:
Same RE
Equal RE
Similar RE
Equivalent RE
Quiz Start Time: 06:37 AM
Time Left 28
sec(s)
Question # 3 of 10 ( Start time: 06:39:53 AM ) Total Marks: 1
Which of the following statement is NOT true?
Select correct option:
FA can be considered to be an NFA
FA can be considered to be an NFA with null string
NFA can be considered to be an TG
TG can be considered to be an NFA
Quiz Start Time: 06:37 AM
Time Left 82
sec(s)
Question # 4 of 10 ( Start time: 06:41:17 AM ) Total Marks: 1
Two FAs are said to be equivalent, if they
Select correct option:
accept null string
accept same language
accept different language
none of the given options
Quiz Start Time: 06:37 AM
Time Left 77
sec(s)
Question # 5 of 10 ( Start time: 06:41:34 AM ) Total Marks: 1
The language having even number of a’s and even number of b’s defined over
S = {a,
b}
is called
Select correct option:
EVEN-EVEN
ODD-ODD
PALINDROME
FACTORIAL
Quiz Start Time: 06:37 AM
Time Left 72
sec(s)
Question # 6 of 10 ( Start time: 06:41:54 AM ) Total Marks: 1
Is the language {a ab aba bab} regular?
Select correct option:
Yes
No
Quiz Start Time: 06:37 AM
Time Left 41
sec(s)
Question # 7 of 10 ( Start time: 06:42:18 AM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must
correspond to the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Quiz Start Time: 06:37 AM
Time Left 69
sec(s)
Question # 8 of 10 ( Start time: 06:43:21 AM ) Total Marks: 1
According to theory of automata there are _________ types of languages
Select correct option:
One
Two
Three
Four
Quiz Start Time: 06:37 AM
Time Left 32
sec(s)
Question # 9 of 10 ( Start time: 06:43:47 AM ) Total Marks: 1
What is false about the term alphabet?
Select correct option:
It is a finite set of symbols.
It is usually denoted by Greek letter sigma
It can be an empty set.
Strings are made up of its elements.
Quiz Start Time: 06:37 AM
Time Left 38
sec(s)
Question # 10 of 10 ( Start time: 06:44:54 AM ) Total Marks: 1
Every FA is a TG.
Select correct option:
True
False
1*(1 + ) = 1* this statement is
True
False
Sometimes true & sometimes false
None of these
Question No: 4 ( Marks: 1 ) - Please choose one
a*b* = (ab)* this expression is __________
True
False
Can’t be assumed
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
a,b
2+
1
a,b
Above given FA can be expressed as ________
(a + b)*
a* + b*
(ab + ba)*
None of these
If a language is expressed through TG, then that language will have its RE.
True
False
Depends on language
None of these
Question No: 8 ( Marks: 1 ) - Please choose one
In TG there may exist more than one path for certain string.
True
False
Depends on the language
None of these
Question No: 9 ( Marks: 1 ) - Please choose one
In TG there may exist no paths for certain string.
True
False
Depends on the language
None of these
Question No: 10 ( Marks: 1 ) - Please choose one
GTG can have _______________ final state.
0
1
More than 1
All of the given
Question No: 12 ( Marks: 1 ) - Please choose one
b
––
+
a,b
Above given TG accepts the language in which all strings
Ends in b
Begins with b
Ends and begins with b
None of the given
Question No: 14 ( Marks: 1 ) - Please choose one
Every FA should be __________
Deterministic
Non- Deterministic
Deterministic & Non- Deterministic
None of these
Question No: 15 ( Marks: 1 ) - Please choose one
If in an NFA,
is allowed to be a label of an edge then that NFA is called _________.
Will not remain NFA
NFA with NFA with null string
Either "NFA with null string" OR "NFA with "
Question No: 17 ( Marks: 1 )
In transition diagram of an FA, how can we represent initail and final states?
Question No: 18 ( Marks: 1 )
How can we say that two REs are equal?
Question No: 19 ( Marks: 2 )
Can you accept the following statement? Or there is a condition to accept it?
For every Mealy machine there is a Moore machine that is equivalent to it.
Question No: 20 ( Marks: 3 )
Let S be all string of a’s and b’s with odd length. What is S*?
Question No: 21 ( Marks: 5 )
Draw FA corresponding to following NFA?
a
1b
ba
2
3
4+
Question No: 22 ( Marks: 10 )
Give the recursive deflations for the following languages over the alphabet {a, b}:
(i) The language EVENSTRING of all words of even length.
(ii) The language ODDSTRING of all words of odd length.
Top of Form
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Quiz Start Time: 07:38 PM
Question # 1 of 10 ( Start time: 07:38:23 PM ) Total Marks: 1
Left hand Side of a Production in CFG may consist of ________
Select correct option:
Exactly one Nonterminal
More than one Nonterminals
Exactly one Terminals
More than one Terminals
Top of Form
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Question # 2 of 10 ( Start time: 07:39:57 PM ) Total Marks: 1
Given a PDA that accepts the language L ______
Select correct option:
There exists a CFG that generates exactly L
There does not exist any CFG that generates exactly L
that PDA will also accept Language L' (complement of L)
None of given options
/wEWBgLtlK62Bw
Bottom of Form
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Top of Form
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Question # 3 of 10 ( Start time: 07:41:13 PM ) Total Marks: 1
Answer the following prefix expression is * * + / 6 3 9 + 3 2 1
Select correct option:
60
55
110
70
/wEWBgK3ruImAr
Top of Form
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Question # 4 of 10 ( Start time: 07:42:02 PM ) Total Marks: 1
The PDA is called non-deterministic PDA when there are more than one out going edges from……… state
Select correct option:
START or READ
POP or REJECT
READ or POP
PUSH or POP
/wEWBgK39NrvDA
Top of Form
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Question # 5 of 10 ( Start time: 07:43:34 PM ) Total Marks: 1
The derivation of a word w, generated by a CFG, such that at each step, a production is applied to the left most nonterminal in
the
working string, is said to be ___________.
Select correct option:
Left most derivation
Right most derivation
Left most Terminal
Right most Terminal
/wEWBgLlu8XcDw
Top of Form
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Question # 6 of 10 ( Start time: 07:44:36 PM )
Total
Marks:
1
In conversion form of PDA there is no……… state
Select correct option:
PUSH
READ
ACCEPT
REJECT
/wEWBgLzu5VsAr
Top of Form
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Time
Left
87
sec(s)
Question # 7 of 10 ( Start time: 07:45:51 PM ) Total Marks: 1
A _________ is the one for which every input string has a unique path through the machine.
Select correct option:
deterministic PDA
nondeterministic PDA
PUSHDOWN store
Input Tape
/wEWBgLo5KLvBA
Top of Form
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Question # 9 of 10 ( Start time: 07:48:35 PM ) Total Marks: 1
Which of the following states is not part of PDA
Select correct option:
START
ACCEPT
WRTITE
REJECT
/wEWBgKTqtKYAg
Top of Form
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Question # 10 of 10 ( Start time: 07:49:01 PM ) Total Marks: 1
Before the CFG corresponding to the given PDA is determined, the PDA is converted into the standard form which is called.
Select correct option:
Finite Automaton
Chomsky Normal Form (CNF)
Conversion form
None of given options
/wEWBgL4j6fiAgK
Bottom of Form
Bottom of Form
Bottom of Form
Bottom of Form
Bottom of Form
Bottom of Form
Bottom of Form
Bottom of Form
Top of Form
/wEPDwUKMTY2N
Question # 1 of 10 ( Start time: 10:20:49 PM ) Total Marks: 1
Halt states are
Select correct option:
Start and Accept
Accept and Reject
Start and Reject
Read and Reject
Top of Form
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Question # 2 of 10 ( Start time: 10:21:30 PM ) Total Marks: 1
The language generated by the CFG is called the language ……by the CFG
Select correct option:
Defined
Derived
Produced
All of the given options
/wEWBgKG/Yz5Dg
Bottom of Form
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Top of Form
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Question # 3 of 10 ( Start time: 10:23:04 PM ) Total Marks: 1
According to Myhill Nerode theorem, if L generates finite no. of classes then L is.......
Select correct option:
Finite
Infinite
Regular
Non regular
/wEWBgKH+qz0A
Top of Form
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Question # 4 of 10 ( Start time: 10:24:27 PM ) Total Marks: 1
A non regular language can be represented by
Select correct option:
RE
FA
TG
None of the given options
/wEWBgLz/I/UDA
Top of Form
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Question # 5 of 10 ( Start time: 10:24:51 PM ) Total Marks: 1
The major problem in the earliest computers was
Select correct option:
To store the contents in the registers
To display mathematical formulae
To load the contents from the registers
To calculate the mathematical formula
/wEWBgLC5+yDC
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Question # 7 of 10 ( Start time: 10:27:11 PM ) Total Marks: 1
In nondeterministic PDA a string is supposed to be accepted, if there exists at least one path traced by the string, leading to
______
state.
Select correct option:
ACCEPT
REJECT
START
READ
Top of Form
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Top of Form
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Question # 10 of 10 ( Start time: 10:29:40 PM ) Total Marks: 1
If an FA has N state then it must accept the word of length
Select correct option:
N-1
N+1
N
2N
/wEWBgKkhuq4D
Top of Form
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Question # 1 of 10 ( Start time: 10:44:30 PM ) Total Marks: 1
PDA stands for ________
Select correct option:
Push and Drop Automaton
Pop and Drop Automaton
Push Down Automaton
None of given options
/wEWBgK70cycBA
Bottom of Form
Top of Form
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Question # 2 of 10 ( Start time: 10:45:45 PM ) Total Marks: 1
By removing null and unit productions:
Select correct option:
CNF can be converted into CFG
CFG can be converted into CNF
CNF can be converted into TG
None of the given options
/wEWBgL08LHOB
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Question # 3 of 10 ( Start time: 10:46:26 PM ) Total Marks: 1
In conversion form of PDA there is no……… state
Select correct option:
PUSH
READ
ACCEPT
REJECT
/wEWBgKf5IKcAw
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Top of Form
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Question # 4 of 10 ( Start time: 10:46:54 PM ) Total Marks: 1
START, READ, HERE and ACCEPT states are called the ____ of the machine.
Select correct option:
Forks
Plugs
Joints
None of given options
/wEWBgLQhbvrD
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Question # 5 of 10 ( Start time: 10:47:29 PM ) Total Marks: 1
In a STACK:
Select correct option:
The element PUSHed first is POPed first
The element PUSHed first is POPed in the last
The element PUSHed in last is POPed in last
None of given options
/wEWBgLr7ZhEAr
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Top of Form
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Question # 6 of 10 ( Start time: 10:48:44 PM ) Total Marks: 1
The tree which produced all the strings of a language is called
Select correct option:
Derivation tree
Ambiguous tree
Total language tree
Non ambiguous tree
/wEWBgLZ6KnfCQ
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Question # 7 of 10 ( Start time: 10:50:06 PM ) Total Marks: 1
The CFG is said to be ambiguous if there exist at least one word of its language that can be generated by the …………
production
trees
Select correct option:
One
Two
More than one
At most one
/wEWBgKm54TfB
Bottom of Form
Top of Form
/wEPDwUKMTY2N
Question # 9 of 10 ( Start time: 10:51:43 PM ) Total Marks: 1
A PDA is in conversion form if it fulfills the following condition:
Select correct option:
There is only one ACCEPT state.
There are more than one ACCEPT states
There is only one REJECT state.
Thre are more than one REJECT states
/wEWBgKP89u8D
Bottom of Form
Top of Form
/wEPDwUKMTY2N
Question # 10 of 10 ( Start time: 10:52:11 PM ) Total Marks: 1
The derivation of a word w, generated by a CFG, such that at each step, a production is applied to the left most nonterminal in
the
working string, is said to be ___________.
Select correct option:
Left most derivation
Right most derivation
Left most Terminal
Right most Terminal
/wEWBgLNlvOfBg
Bottom of Form
Bottom of Form
Top of Form
/w EPDw UKMTY2
Question # 5 of 10 ( Start time: 11:06:30
PM )
Total Marks:
1
Identify the FALSE statement about following CFG: S
-> SB|AB A -> CC B -> b C -> a
Select correct option:
CFG generates NULL string
CFG is not in CNF
CFG has 8 Nonterminals
All of the given options
Question # 4 of 10 ( Start time: 11:05:39
PM )
Total Marks:
1
Before the CFG corresponding to the given PDA is
determined, the PDA is converted into the standard
form which is called.
Select correct option:
Finite Automaton
Chomsky Normal Form (CNF)
Conversion form
None of given options
Question # 6 of 10 ( Start time: 11:07:04
PM )
Total Marks:
1
The reverse of the string sbfsbb over { sb, f, b }
Select correct option:
bbsfbs
bsbfsb
sbbfsb
bsfbsb
Question # 3 of 10 ( Start time: 11:04:57
PM )
Total Marks:
1
Two languages are said to belong to same class if they
end in the same state when they run over an FA, that
state
Select correct option:
Must be final state
May be final state or not
May be start state or not
None of the given option
Question # 9 of 10 ( Start time: 11:04:57
PM )
Total Marks:
1
All languages can be generated by the CFG.
Select correct option:
True
False
Question # 10 of 10 ( Start time: 10:38:00 PM
)
Total Marks:
1
The input string is placed, before it runs, in
Select correct option:
Stack
Memory
Tape
Ram
Question # 4 of 10 ( Start time: 10:32:44 PM ) Total Marks: 1
In CFG, the symbols that cannot be replaced by anything are
called
Select correct option:
Terminals
Non terminals
Productions
None of the given options
Quiz Start Time: 10:30 PM
Time Left 90
sec(s)
Question # 2 of 10 ( Start time: 10:31:15 PM ) Total Marks: 1
If L1 and L2 are regular languages then which statement is
NOT true?
Select correct option:
L1 + L2 is always regular
L1 L2 is always regular
L1/L2 is always regular
L1* is always regular
Time Left 90
sec(s)
Question # 3 of 10 ( Start time: 10:31:31
PM ) Total Marks: 1
uced all the strings of a language is called
Select correct option:
Derivation tree
Ambiguous tree
Total language tree
Non ambiguous tree
Question # 8 of 10 ( Start time:
10:35:28 PM ) Total Marks: 1
The part of an FA, where the input string is placed before it is run, is
called _______
Select correct option:
State
Transition
Input Tape
Output Tape
Question # 1 of 10 ( Start time:
10:30:58 PM ) Total Marks: 1
By removing null and unit productions:
Select correct option:
CNF can be converted into CFG
CFG can be converted into CNF
CNF can be converted into TG
None of the given options
Bottom of Form
Top of Form
/wEPDwUKMTY2N
Question # 1 of 10 ( Start time: 07:38:23 PM ) Total Marks: 1
Left hand Side of a Production in CFG may consist of ________
Select correct option:
Exactly one Nonterminal
More than one Nonterminals
Exactly one Terminals
More than one Terminals
Top of Form
/wEPDwUKMTY2N
Question # 2 of 10 ( Start time: 07:39:57 PM ) Total Marks: 1
Given a PDA that accepts the language L ______
Select correct option:
There exists a CFG that generates exactly L
There does not exist any CFG that generates exactly L
that PDA will also accept Language L' (complement of L)
None of given options
/wEWBgLtlK62Bw
Bottom of Form
/wEWBgKJoZuiDA
Top of Form
/wEPDwUKMTY2N
Question # 3 of 10 ( Start time: 07:41:13 PM ) Total Marks: 1
Answer the following prefix expression is * * + / 6 3 9 + 3 2 1
Select correct option:
60
55
110
70
/wEWBgK3ruImAr
Top of Form
/wEPDwUKMTY2N
Question # 4 of 10 ( Start time: 07:42:02 PM ) Total Marks: 1
The PDA is called non-deterministic PDA when there are more than one out going edges from……… state
Select correct option:
START or READ
POP or REJECT
READ or POP
PUSH or POP
/wEWBgK39NrvDA
Top of Form
/wEPDwUKMTY2N
Question # 5 of 10 ( Start time: 07:43:34 PM ) Total Marks: 1
The derivation of a word w, generated by a CFG, such that at each step, a production is applied to the left most nonterminal in
the
working string, is said to be ___________.
Select correct option:
Left most derivation
Right most derivation
Left most Terminal
Right most Terminal
/wEWBgLlu8XcDw
Top of Form
/wEPDwUKMTY2N
Question # 6 of 10 ( Start time: 07:44:36 PM )
Total
Marks:
1
In conversion form of PDA there is no……… state
Select correct option:
PUSH
READ
ACCEPT
REJECT
/wEWBgLzu5VsAr
Top of Form
/wEPDwUKMTY2N
Question # 7 of 10 ( Start time: 07:45:51 PM ) Total Marks: 1
A _________ is the one for which every input string has a unique path through the machine.
Select correct option:
deterministic PDA
nondeterministic PDA
PUSHDOWN store
Input Tape
/wEWBgLo5KLvBA
Top of Form
/wEPDwUKMTY2N
Question # 9 of 10 ( Start time: 07:48:35 PM ) Total Marks: 1
Which of the following states is not part of PDA
Select correct option:
START
ACCEPT
WRTITE
REJECT
/wEWBgKTqtKYAg
Top of Form
/wEPDwUKMTY2N
Question # 10 of 10 ( Start time: 07:49:01 PM ) Total Marks: 1
Before the CFG corresponding to the given PDA is determined, the PDA is converted into the standard form which is called.
Select correct option:
Finite Automaton
Chomsky Normal Form (CNF)
Conversion form
None of given options
MIDTERM FALL 2010
[email protected]
Dated 08-12-2010 (3st session)
CS402
Question No: 1 (Marks: 1) - Please choose one
Auto Meta mean
• Manual work
• Automatic work
Question No: 2 (Marks: 1) - Please choose one
S= {a,bc,cc} has the latters
•1
•2
•3
•4
Question No: 3 (Marks: 1) - Please choose one
S={a,bb,bab,baabb} set of strings then S* will not have
• Baba
• Baabbab
• Bbaaabb
• bbbaabaabb(not confirmed)
Question No: 4 (Marks: 1) - Please choose one
One language can represents more then one RE.
• True
• Falss
• Can’t be assumed
• Non of given
Question No: 5 (Marks: 1) - Please choose one
Given GTG has RE
• (a+b)* (aa+bb)(a+b)*
• None of option
Question No: 6 (Marks: 1) - Please choose one
•b
• babab
• baaab
• all
NFA accept String
Question No:7 (Marks: 1) - Please choose one
• bab
•a
• aba
• a & aba
NFA accept String
Question No: 8 (Marks: 1) - Please choose one
• (a+b)*
• Λ+(a+b)*a
• Λ+(a+b)*a*
• None of given
TG has
Question No: 9 (Marks: 1) - Please choose one
TG can more then one initial state
• True
• False
• Depend on alphabets
• None of given
Question No:10 (Marks: 1) - Please choose one
• (a+b)*
• (a+b)*(a*+b*)
• None of the given
Question No: 11 (Marks: 1) - Please choose one
The clouser FA*(on an FA ) always accept _string
• Null
• aa
• bb
• None of given
Question No: 12 (Marks: 1) - Please choose one
In FA final state represent by sign
•+
••=
•*
Question No: 13 (Marks: 1) - Please choose one
RE will be
In FA one enter in specific stat but there is no way to leave it then state is called
• Dead States
• Waste Baskets
• Davey John Lockers
• All of above
Question No: 14 (Marks: 1) - Please choose one
Using tree structure final state represent by
•*
•• double circle
• None of given
Question No: 15 (Marks: 1) - Please choose one
• a’s occur only in even clumps and that ends in three or more b’s
• length larger then 2
• it does not accept any language
• none of given option
Question No: 16 (Marks: 1) - Please choose one
• Equal
• Not equal
• Not valid
• None of given
These GTG are
Question No: 17 (Marks: 1) - Please choose one
to FA will
• Equal
• Not equal
• Not valid
• None of given
NFA
Question No: 18 (Marks: 1) - Please choose one
FA having RE
K + a + b + (a+b)*(ab+ba+bb).
Question No: 19 (Marks: 1) - Please choose one
Question No: 20 (Marks: 1) - Please choose one
Question No: 21 (Marks: 2) - Please choose one
The language can express in FA then why we need NFA. Justify your answer.
Question No: 22 (Marks: 2) - Please choose one
Names of four type of autometa.
Question No: 23 (Marks: 3) - Please choose one
Check the given statements or correct or not if not then correct it.
1. String in regular language can not be infinite
2. Concatenation of finite letters from alphabets called sigma
3. There cannot be more then on FA,s for same language.
Question No: 24 (Marks: 3) - Please choose one
How can we know, what language a certain RE represent
Question No: 25 (Marks: 5) - Please choose one
Explain mealy machine
Question No: 26 (Marks: 5) - Please choose one
Show the transition table of FA1+FA2
Answer
Identify the FALSE statement about following CFG: S -> SB|AB A -> CC B -> b C -> a
Select correct option:
CFG generates NULL string
CFG is not in CNF
CFG has 8 Nonterminals
All of the given options
Question # 3 of 10 ( Start time: 10:44:58 AM ) Total Marks: 1
Answer the following prefix expression is * * + / 6 3 9 + 3 2 1
Select correct option:
60
55
110
70
Question # 4 of 10 ( Start time: 10:46:18 AM ) Total Marks: 1
In new format of an FA (discussed in lecture 37),This state is like a final state of an FA
Select correct option:
ACCEPT
REJECT
START
READ
Question # 5 of 10 ( Start time: 10:47:44 AM ) Total Marks: 1
The CFG which generates the regular language is called
Select correct option:
Regular expression
Finite Automata
Regular grammar
None of the given options
Question # 6 of 10 ( Start time: 10:48:56 AM ) Total Marks: 1
The locations into which we put the input letters on "Input Tap" are called __________
Select correct option:
words
alphabets
cells
elements
Question # 7 of 10 ( Start time: 10:50:24 AM ) Total Marks: 1
Given a PDA that accepts the language L ______
Select correct option:
There exists a CFG that generates exactly L
There does not exist any CFG that generates exactly
that PDA will also accept Language L' (complement of
None of given options
Question # 8 of 10 ( Start time: 10:51:20 AM ) Total Marks: 1
Before the CFG corresponding to the given PDA is determined, the PDA is converted into the standard form which is
called.
Select correct option:
Finite Automaton
Chomsky Normal Form (CNF)
Conversion form
None of given options
Question # 9 of 10 ( Start time: 10:52:42 AM ) Total Marks: 1
The major problem in the earliest computers was
Select correct option:
To
To
To
To
store the contents in the registers
display mathematical formulae
load the contents from the registers
calculate the mathematical formula
Question # 10 of 10 ( Start time: 10:53:33 AM ) Total Marks: 1
Consider the Following CFG: (NOTE: ^ means NULL) S->Xa X->aX|bX|^ above given CFG can be represented by RE
_________
Select correct option:
a*b*
a*b*a
(a+b)*a
a(a+b)*a
Quiz No.1
Question # 1 of 10 ( Start time: 06:45:47 PM ) Total Marks: 1
By removing null and unit productions:
Select correct option:
CNF can be converted into CFG
CFG can be converted into CNF
CNF can be converted into TG
None of the given options
Question # 2 of 10 ( Start time: 06:46:29 PM ) Total Marks: 1
Null production is a
Select correct option:
Word
String
Terminal
All of the given options
Question # 3 of 10 ( Start time: 06:47:04 PM ) Total Marks: 1
consider the CFG given below: S->A|bb A->B|b B->S|a Unit Production(s) in above CFG
is/are _______
Select correct option:
S->A
A->B
B->S
All of given options
Question # 4 of 10 ( Start time: 06:48:33 PM ) Total Marks: 1
To write the expression from the tree, it is required to traverse from
Select correct option:
Top to bottom of the tree
Left side of the tree
Bottom to top of the tree
Right side of the tree
Question # 5 of 10 ( Start time: 06:50:02 PM ) Total Marks: 1
If a CFG has a null production, then it is ______
Select correct option:
Posiible to construct another CFG without null production accepting the same language with
the exception of the word ^
Not possible to construct another CFG without null production accepting the same language
with the exception of the word ^
Called NULL CFG
Called Chmosky Normal Form (CNF)
Question # 6 of 10 ( Start time: 06:51:14 PM ) Total Marks: 1
The tree which produced all the strings of a language is called
Select correct option:
Derivation tree
Ambiguous tree
Total language tree
Non ambiguous tree
Question # 7 of 10 ( Start time: 06:51:39 PM ) Total Marks: 1
A PDA consists of the following:
Select correct option:
An alphabet (Sigma) of input letters.
An input TAPE with infinite many locations in one direction
One START state with only one out-edge and no in-edge
All of the given options
Question # 8 of 10 ( Start time: 06:52:32 PM ) Total Marks: 1
The derivation of a word w, generated by a CFG, such that at each step, a production is
applied to the left most nonterminal in the working
string, is said to be ___________.
Select correct option:
Left most derivation
Right most derivation
Left most Terminal
Right most Terminal
Question # 9 of 10 ( Start time: 06:53:06 PM ) Total Marks: 1
A PDA is called nondeterministic PDA if ___________
Select correct option:
There are more than one outgoing edges at READ or POP states with one label
There are more than one PUSH states
There are mroe than one POP states
All of the given options
Question # 10 of 10 ( Start time: 06:54:18 PM ) Total Marks: 1
In new format of an FA (discussed in lecture 37),This state is like a final state of an FA
Select correct option:
ACCEPT
REJECT
START
READ
Quiz No.2
Question # 1 of 10 ( Start time: 07:16:01 PM ) Total Marks: 1
Identify FALSE statement:
Select correct option:
Every Regular Expression be expressed by CFG and every CFG can be expressed by a
Regular Expression
Every regular expression can be expressed as CFG but every CFG cannot be expressed as a
regular expression.
For a PDA, there exists a CFG, that represents the same language as represented by PDA.
None of the given options
Question # 2 of 10 ( Start time: 07:17:29 PM ) Total Marks: 1
In a CFG the nonterminal that occurs first from the left in the working string, is said to be
________
Select correct option:
Least Significant nonterminal
Most Significant nonterminal
Left most nonterminal
Left most derivate
Question # 3 of 10 ( Start time: 07:18:27 PM ) Total Marks: 1
If a CFG has only productions of the form nonterminal -> string of two nonterminals or
nonterminal -> one terminal then the CFG is said to
be in _________
Select correct option:
PDA form
Chomsky Normal Form (CNF)
NULL able form
Unit production form
Question # 4 of 10 ( Start time: 07:18:58 PM ) Total Marks: 1
Consider the following CFG: (NOTE: ^ means NULL) S->a|Xb|aYa X->Y|^ Y->b|X Which
Nonterminals are nullable
Select correct option:
S and X
X and Y
Y and S
S,X and Y
Question # 5 of 10 ( Start time: 07:20:28 PM ) Total Marks: 1
A PDA is in conversion form if it fulfills the following condition:
Select correct option:
There is only one ACCEPT state.
There are more than one ACCEPT states
There is only one REJECT state.
Thre are more than one REJECT states
Question # 6 of 10 ( Start time: 07:21:02 PM ) Total Marks: 1
The CFG which generates the regular language is called
Select correct option:
Regular expression
Finite Automata
Regular grammar
None of the given options
Question # 7 of 10 ( Start time: 07:22:17 PM ) Total Marks: 1
PDA stands for ________
Select correct option:
Push and Drop Automaton
Pop and Drop Automaton
Push Down Automaton
None of given options
Question # 8 of 10 ( Start time: 07:22:41 PM ) Total Marks: 1
___________ states are called the halt states.
Select correct option:
ACCEPT and REJECT
ACCEPT and READ
ACCEPT AND START
ACCEPT AND WRITE
Question # 9 of 10 ( Start time: 07:23:01 PM ) Total Marks: 1
The CFG S --> aSa | bSb | a | b | ^ represents the language
Select correct option:
EVEN-EVEN
PALINDROM
EQUAL
ODD-ODD
Question # 10 of 10 ( Start time: 07:24:34 PM ) Total Marks: 1
which path sequence follows the rules of "conversion form" of "PDA"
Select correct option:
READ -> POP -> POP
POP -> POP -> POP
READ -> POP -> PUSH a
HERE -> PUSH a -> PUSH a
Quiz No.3
Question # 1 of 10 ( Start time: 07:34:23 PM ) Total Marks: 1
Identify the TRUE statement about following CFG: S -> SB|AB A -> CC B -> b C -> a
Select correct option:
The given CFG has 8 Nonterminals
The given CFG has 8 Terminals
The given CFG is in CNF
The given CFG is not in CNF
Question # 2 of 10 ( Start time: 07:35:29 PM ) Total Marks: 1
To write the expression from the tree, it is required to traverse from
Select correct option:
Top to bottom of the tree
Left side of the tree
Bottom to top of the tree
Right side of the tree
Question # 4 of 10 ( Start time: 07:36:26 PM ) Total Marks: 1
A PDA is not in conversion form if ___________
Select correct option:
There are more than one ACCEPT states
There are more than one REJECT states
Every READ or HERE is followed immediately by a PUSH
All of given options
Question # 5 of 10 ( Start time: 07:37:02 PM ) Total Marks: 1
The PDA is called non-deterministic PDA when there are more than one out going edges
from……… state
Select correct option:
START or READ
POP or REJECT
READ or POP
PUSH or POP
Question # 6 of 10 ( Start time: 07:38:12 PM ) Total Marks: 1
In new format of an FA (discussed in lecture 37), This state is like dead-end non final state
Select correct option:
ACCEPT
REJECT
START
READ
Question # 8 of 10 ( Start time: 07:38:50 PM ) Total Marks: 1
Consider the following CFG: (NOTE: ^ means NULL) S->a|Xb|aYa X->Y|^ Y->b|X Which
Nonterminal(s) is/are NOT nullable
Select correct option:
S
X
Y
S,X and Y
Question # 9 of 10 ( Start time: 07:39:57 PM ) Total Marks: 1
The PDA which is in the conversion form can be supposed to be the _________ with path
segments in between, similar to a TG.
Select correct option:
Set of joints
Set of Forks
Set of Plugs
None of given options
(a* + b*)* = (a + b)* this expression is __________
T
F
If S = { x }, then S* will be
{x,xx,xxx,xxxx,…}
{^ ,x,xx,xxx,xxxx,…}
The states in which there is no way to leave after entry are called
Davey John Lockers
Dead States
Waste Baskets
All of the given options
If S = {ab, bb}, then S* will not contain
Abbbab
Bbba
ababbb
bbbbab
According to theory of automata there are _________ types of languages
1
2
3
4
What do automata mean?
Something done manually
Something done automatically
What is false about the term alphabet?
It is a finite set of symbols.
It is usually denoted by Greek letter sigma
It can be an empty set.
Strings are made up of its elements
Formal is also known as _________
Syntactic language
Semantic language
Informal language
None of these
Kleene star closure can be defined
Over any set of string
Over specific type of string
While finding RE corresponding to TG, we connect the new start state to the old start state by the transition labeled by
A
B
null string
None of the given options
1) Can we use only the + and – symbols to show the initial and final states of the
FA…… Marks2
2) State that the followings are true or false. … Marks2
a. Kleen star and Kleen closure are different.
b. Length of the output of the mealy machine is one less than the input string.
3) For mealy machine tell about _, _ and what this machine will do. … Marks3
4) Name the two methods of the Kleen’s theorem part III. … Marks3
5) Explain Moore Machine… Marks5
6) Show that two TG accept the same language of event number of states. … Marks5
an other paper
1) State that the followings are true or false. … Marks2
a. Kleen star and Kleen closure are different.
b. Length of the output of the mealy machine is one less than the input string.
2) complement melay machine (tataly) 2marks
3) one similtary and disimilarty in the DFA and FA
4) make the union of the given FAs (from hand out fist example)
5) diffrance between the TG FA and GTG
Formal is known as Syntactic language.
length of even even language is always even.
While finding RE corresponding to TG we connect the new start state with the old start state
by transition labeled by a null string.
Question # 1 of 10 ( Start time: 05:46:41 PM ) Total Marks: 1
While finding RE corresponding to TG, If TG has more than one start state then
Select correct option:
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start state
by the transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b. (ba+a)*
c. a*(aa*b)* d. (a*b*)*
a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*.
{ x}*, { x}+, {a+b}*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must correspond
to the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Question # 1 of 10 ( Start time: 11:12:33 PM ) Total Marks: 1
Alphabet S = {a, bc, cc} has _______ number of letters
Select correct option:
One
Two
Three
Four
Question # 2 of 10 ( Start time: 11:14:03 PM ) Total Marks: 1
If S = { x }, then S* will be
{x,xx,xxx,xxxx,…}
{^ ,x,xx,xxx,xxxx,…}
Question # 3 of 10 ( Start time: 11:15:11 PM ) Total Marks: 1
Length of EVEN-EVEN language is _________
Select correct option:
Even
Odd
Sometimes even & sometimes odd
Such language doesn’t exist
Question # 4 of 10 ( Start time: 11:16:41 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Question # 5 of 10 ( Start time: 11:17:26 PM ) Total Marks: 1
If S = {aa, bb}, then S* will not contain
Aabbaa
Bbaabbbb
Aaabbb
aabbaaaa
Question # 6 of 10 ( Start time: 11:18:55 PM ) Total Marks: 1
Formal is also known as _________
Syntactic language
Semantic language
Informal language
None of these
Question # 7 of 10 ( Start time: 11:20:15 PM ) Total Marks: 1
In an FA, when there is no path starting from initial state and ending in final state then that FA
accept null string
accept all strings
accept all non empty strings
does not accept any string
Question # 9 of 10 ( Start time: 11:22:33 PM ) Total Marks: 1
FA of EVEN language shows null string when
Initial state is final as well
EVEN does not accept null
One state is declared null
None of the these
NEW Modified
CS402-Theory of Automata MCQs
Lecture 23- 35 SOLVED By 0300-6986459
21) For a given input, it provides the compliment of Boolean AND output.
NAND box (NOT AND)
DELAY box
OR box
AND box
22) It delays the transmission of signal along the wire by one step (clock pulse).
NAND box (NOT AND)
DELAY box
OR box
AND box
23) For the given input, it provides the Boolean OR output
NAND box (NOT AND)
DELAY box
OR box
AND box
24) For the given input, AND box provides the Boolean AND output.
True False
25) The current in the wire is indicated by 1 and 0 indicates the absence of the
current.
True False
26) Any language that can not be expressed by a RE is said to be regular language.
True False
27) If L1 and L2 are regular languages is/are also regular language(s).
L1 + L2
L1L2
L1*
All of above
28) Let L be a language defined over an alphabet Σ, then the language of strings,
defined over Σ, not belonging to L, is called Complement of the language L,
denoted by Lc or L’.
True False
29) To describe the complement of a language, it is very important to describe the ---------- of that language over which the language is defined.
Alphabet
Regular Expression
String
Word
30) For a certain language L, the complement of Lc is the given language L i.e.
(Lc)c = Lc
True False
31) If L is a regular language then, --------- is also a regular language.
Lm Ls Lx Lc
32) Converting each of the final states of F to non-final states and old non-final
states of F to final states, FA thus obtained will reject every string belonging to
L and will accept every string, defined over Σ, not belonging to L. is called
Transition Graph of L
Regular expression of L
Complement of L
Finite Automata of L
33) If L1 and L2 are two regular languages, then L1 U L2 is not a regular.
True False
34) De-Morgan's law for sets is expressed by,
1 2 1 2 (L c ∩L c )c = L c ∩L c
1 2 1 2 (L c ∩L c )c = L c ∩L c
1 2 1 2 (L c ∩L c )c = L ∩L
1 2 1 2 (L c ∩L c )c = L ∪L CORRECT
35) If L1 and L2 are regular languages, then these can be expressed by the
corresponding FAs.
True False
36) L= language of words containing even number of a’s. Regular Expression is
(a+b)*aa(a+b)*
(b+ab*a)*
a+bb*aab*a
(a+b)*ab(a+b)*
37) The regular expression defining the language L1 U L2 can be obtained,
converting and reducing the previous ------------- into a ------------ as after
eliminating states.
GTG, TG
FA, GTG
FA, TG
TG, RE
38) The language that can be expressed by any regular expression is called a Non
regular language.
True False
39) The languages -------------- are the examples of non regular languages.
PALINDROME and PRIME
PALINDROME and EVEN-EVEN
EVEN-EVEN and PRIME
FACTORIAL and SQURE
40) Let L be any infinite regular language, defined over an alphabet Σ then there
exist three strings x, y and z belonging to Σ* such that all the strings of the
form xynz for n=1,2,3, … are the words in L. called.
Complement of L
Pumping Lemma
Kleene’s theorem
None in given
(21) Languages are proved to be regular or non regular using pumping lemma.
True False
(22) ------------------- is obviously infinite language.
EQUAL-EQUAL
EVEN-EVEN
PALINDROME
FACTORIAL
(23) If, two strings x and y, defined over Σ, are run over an FA accepting the
language L, then x and y are said to belong to the same class if they end in the
same state, no matter that state is final or not.
True False
(29) Myhill Nerode theorem is consisting of the followings,
L partitions Σ* into distinct classes.
If L is regular then, L generates finite number of classes.
If L generates finite number of classes then L is regular.
All of above
(30) The language Q is said to be quotient of two regular languages P and R,
denoted by--- if PQ=R.
R=Q/P Q=R/P Q=P/R P=R/Q
(31) If two languages R and Q are given, then the prefixes of Q in R denoted by
Pref(Q in R).
True False
(27) Let Q = {aa, abaaabb, bbaaaaa, bbbbbbbbbb} and R = {b, bbbb, bbbaaa,
bbbaaaaa} Pref (Q in R) is equal to,
{b,bbba,bbbaaa}
{b,bba,bbaaa}
{ab,bba,bbbaa}
{b,bba,bbba}
(32) If R is regular language and Q is any language (regular/ non regular), then
Pref (Q in R) is ---------.
Non-regular
Equal
Regular
Infinite
(33) "CFG" stands for _________
Context Free Graph
Context Free Grammar
Context Finite Graph
Context Finite Grammar
(29) ___________ states are called the halt states.
ACCEPT and REJECT
ACCEPT and READ
ACCEPT AND START
ACCEPT AND WRITE
(30) The part of an FA, where the input string is placed before it is run, is called
_______
State
Transition
Input Tape
Output Tape
(35) In new format of an FA (discussed in lecture 37), This state is like dead-end
non final state
ACCEPT
REJECT
STATR
READ
(36) For language L defined over {a, b}, then L partitions {a, b}* into ……
classes
Infinite
Finite
Distinct
Non-distinct
(37) The major problem in the earliest computers was
To store the contents in the registers
To display mathematical formulae
To load the contents from the registers
To calculate the mathematical formula
(38) Between the two consecutive joints on a path
One character can be pushed and one character can be popped
Any no. of characters can be pushed and one character can be popped
One character can be pushed and any no. of characters can be popped
Any no. of characters can be pushed and any no. of characters can be popped
(35) In pumping lemma theorem (x y^n z) the range of n is
n=1, 2, 3, 4……….
n=0, 1, 2, 3, 4……….
n=…….-3,-2,-1, 0, 1, 2, 3, 4……
n=…….-3,-2,-1, 1, 2, 3, 4……
(36) The PDA is called non-deterministic PDA when there are more than one out
going edges from……… state
START or READ
POP or REJECT
READ or POP
PUSH or POP
(49) Identify the TRUE statement:
A PDA is non-deterministic, if there are more than one READ states in PDA
A PDA is never non-deterministic
Like TG, A PDA can also be non-deterministic
A PDA is non-deterministic, if there are more than one REJECT states in PDA
(50) There is a problem in deciding whether a state of FA should be marked or
not when the language Q is infinite.
True False
(51) If an effectively solvable problem has answered in yes or no, then this
solution is called --------Decision procedure
Decision method
Decision problem
Decision making
(52) The following problem(s) ------------- is/are called decidable problem(s).
The two regular expressions define the same language
The two FAs are equivalent
Both a and b
None of given
(53) To examine whether a certain FA accepts any words, it is required to seek
the paths from ------- state.
Final to initial
Final to final
Initial to final
Initial to initial
(54) The high level language is converted into assembly language codes by a
program called compiler.
TRUE FALSE
(55) Grammatical rules which involve the meaning of words are called -------------Semantics
Syntactic
Both a and b
None of given
(56) Grammatical rules which do not involve the meaning of words are called -------------Semantics
Syntactic
Both a and b
None of given
(57) The symbols that can’t be replaced by anything are called -----------------
Productions
Terminals
Non-terminals
All of above
(58) The symbols that must be replaced by other things are called __________
Productions
Terminals
Non-terminals
None of given
(47) The grammatical rules are often called_____________
Productions
Terminals
Non-terminals
None of given
(59) The terminals are designated by ________ letters, while the non-terminals
are designated by ________ letters.
Capital, bold
Small, capital
Capital, small
Small, bold
(60) The language generated by __________ is called Context Free Language
(CFL).
FA TG CFG TGT
(49) Σ = {a,b} Productions S→XaaX X→aX X→bX
X→Λ
This grammar defines the language expressed by___________
(a+b)*aa(a+b)*
(a+b)*a(a+b)*a
(a+b)*aa(a+b)*aa
(a+b)*aba+b)*
(50) S → aXb|b XaX → aX|bX|Λ The given CFG generates the language in
English __________
Beginning and ending in different letters
Beginning and ending in same letter
Having even-even language
None of given
(51) The CFG is not said to be ambiguous if there exists atleast one word of its
language that can be generated by the different production trees,
TRUE FALSE
(54) The language generated by that CFG is regular if _________
No terminal → semi word
No terminal → word
Both a and b
None of given
(55) The production of the form no terminal → Λ is said to be null production.
TRUE FALSE
(54) A production is called null able production if it is of the form N → Λ
TRUE FALSE
(55) The productions of the form nonterminal → one nonterminal, is called
_________
Null production
Unit production
Null able production
None of given
(56) CNF is stands for
Context Normal Form
Complete Normal Form
Chomsky Normal Form
Compared Null Form
FINALTERM EXAMINATION
CS402- Theory of Automata (Session - 1)
Question No: 1 ( Marks: 1 ) - Please choose one
If r1 = (aa + bb) and r2 = ( a + b) then the language (aa + bb)(a + b) will be generated by
► (r1)(r2)
*► (r1 + r2)
► (r2)(r1)
► (r1)*
Question No: 2 ( Marks: 1 ) - Please choose one
“One language can be expressed by more than one FA”. This statement is ______
* ► True
► False
► Some times true & sometimes false
► None of these
Question No: 3 ( Marks: 1 ) - Please choose one
Who did not invent the Turing machine?
► Alan Turing
*► A. M. Turing
► Turing
► None of these
Question No: 4 ( Marks: 1 ) - Please choose one
Which statement is true?
*► The tape of turing machine is infinite.
► The tape of turing machine is finite.
► The tape of turing machine is infinite when the language is regular
► The tape of turing machine is finite when the language is nonregular.
Question No: 5 ( Marks: 1 ) - Please choose one
A regular language:
*► Must be finite
► Must be infinite
► Can be finite or infinite
► Must be finite and cannot be infinite
Question No: 6 ( Marks: 1 ) - Please choose one
Every regular expression can be expressed as CFG but every CFG cannot be expressed as a
regular expression. This statement is:
► Depends on the language
► None of the given options
*► True
► False
Question No: 7 ( Marks: 1 ) - Please choose one
ab
a
X1–
b
X2+
Above given FA corresponds RE r. then FA corresponding to r* will be
a
b
b
z3+
a
z2
z1±
ba
This statement is
*► True
► False
► Depends on language
► None of these
Question No: 8 ( Marks: 1 ) - Please choose one
Consider the language L of strings, defined over Σ = {a,b}, ending in a
► There are finite many classes generated by L, so L is regular
*► There are infinite many classes generated by L, so L is regular
► There are finite many classes generated by L, so L is non-regular
► There are infinite many classes generated by L, so L is non-regular
Question No: 9 ( Marks: 1 ) - Please choose one
ab,ba
ab,ba
±
aa,bb aa,bb
Above given TG has _____________ RE.
► (aa+aa+(ab+ab)(aa+ab)*(ab+ba))*
*► (aa+bb+(ab+ba)(aa+bb)*(ab+ba))*
► (aa+bb+(ab+ba)(aa+bb)(ab+ba))*
► None of these
Question No: 10 ( Marks: 1 ) - Please choose one
The word ‘formal’ in formal languages means
*► The symbols used have well defined meaning
► They are unnecessary, in reality
► Only the form of the string of symbols is significant
► None of these
Question No: 11 ( Marks: 1 ) - Please choose one
Let A = {0, 1}. The number of possible strings of length ‘n’ that can be formed by the
elements of the set A is
► n!
*► n2
► nm
► 2n
Question No: 12 ( Marks: 1 ) - Please choose one
Choose the correct statement.
► A Mealy machine generates no language as such
► A Moore machine generates no language as such
*► A Mealy machine has no terminal state
► All of these
Question No: 13 ( Marks: 1 ) - Please choose one
TM is more powerful than FSM because
► The tape movement is confined to one direction
*► It has no finite state control
► It has the capability to remember arbitrary long sequences of input symbols
► None of these
Question No: 14 ( Marks: 1 ) - Please choose one
If L1 and L2 are expressed by regular expressions r1 and r2, respectively then the language
expressed by r1 + r2 will be _________
* ► Regular
► Ir-regular
► Can’t be decided
► Another Language which is not listed here
Question No: 15 ( Marks: 1 ) - Please choose one
Like TG, a PDA can also be non-deterministic
► True
*► False
Question No: 16 ( Marks: 1 ) - Please choose one
The above machine is a/anTG ___________
► Finite Automata
*► Turing machine
► FA
► TG
Question No: 17 ( Marks: 1 ) - Please choose one
The language of all words (made up of a’s and b’s) with at least two a’s can not be described
by the regular expression.
► a(a+b)*a(a+b)*(a+b)*ab*
► (a+b)* ab* a(a+b)*
► b*ab* a(a+b)*
► none of these
Question No: 18 ( Marks: 1 ) - Please choose one
In FA, if one enters in a specific state but there is no way to leave it, then that specific state
is called
*► Dead State
► Waste Basket
► Davey John Locker
► All of these
Question No: 19 ( Marks: 1 ) - Please choose one
If L is a regular language then, Lc is also a _____ language.
*► Regular
► Non-regular
► Regular but finite
► None of the given
Question No: 20 ( Marks: 1 ) - Please choose one
In CFG, the symbols that can’t be replaced by anything are called___
► Terminal
► Non-Terminal
*► Production
► All of given
Question No: 21 ( Marks: 1 ) - Please choose one
Which of the following is NOT a regular language?
► String of 0’s whose length is a perfect squere
*► Set of all palindromes made up of 0’s and 1’s
► String of 0’s whose length is a prime number
► All of the given options
Question No: 22 ( Marks: 1 ) - Please choose one
Choose the incorrect (FALSE) statement.
► A Mealy machine generates no language as such
► A Mealy machine has no terminal state
*► For a given input string, length of the output string generated by a Moore
machine is not more than the length of the output string generated by that of a Mealy
machine
► All of these
Question No: 23 ( Marks: 1 ) - Please choose one
Pumping lemma is generally used to prove that:
► A given language is infinite
*► A given language is not regular
► Whether two given regular expressions of a regular language are equivalent or not
► None of these
Question No: 24 ( Marks: 1 ) - Please choose one
Which of the following is a regular language?
► String of odd number of zeroes
► Set of all palindromes made up of 0’s and 1’s
*► String of 0’s whose length is a prime number
► All of these
Question No: 25 ( Marks: 1 ) - Please choose one
Choose the incorrect statement:
► (a+b)*aa(a+b)* generates Regular language.
► A language consisting of all strings over Σ={a,b} having equal number of a’s and b’s
is a regular language
► Every language that can be expressed by FA can also be expressed by RE
► None of these
Question No: 26 ( Marks: 1 ) - Please choose one
Left hand side of a production in CFG consists of:
► One terminal
► More than one terminal
► One non-terminal
* ► Terminals and non-terminals
Question No: 27 ( Marks: 2 )
Diffrentiate between Regular and Non regular languages?
Ans:
The main difference between regular and non regular language are as:
1. The regular language is that language which can be expressed by RE is known as regular
language whereas any language which can not be expressed by RE is known as non regular
language.
Question No: 28 ( Marks: 2 )
What is meant by a "Transition" in FA?
Question No: 29 ( Marks: 2 )
What are the halt states of PDAs?
Ans:
There are some halts states in PDA which are as:
1. Accept or reject stat is also halt state.
2. Reject state is like dead non final state.
3. Accept state is like final state.
Question No: 30 ( Marks: 2 )
Identify the null productions and nullable productions from the following CFG:
S -> ABAB
A -> a | /\
B-> b | /\
Question No: 31 ( Marks: 3 )
Describe the POP operation and draw symbol for POP state in context of Push down stack.
Question No: 32 ( Marks: 3 )
What does the the following tape of turing machine show?
READ9 READ3 b b abb 11
ROW
Number
PUSH
What
POP
What
READ
What
TO
Where
FROM
Where
Ans:
Arbitrary Summary Table:
The arbitrary summary table shows the trip from READ9 to READ3 does not pop one
letter form the STACK it adds two letters to the STACK.
Row11 can be concatenated with some other net style sentences e.g. row11 net(READ3,
READ7, a)Net(READ7, READ1, b)Net(READ1, READ8, b) it gives the non terminal
Net(READ9, READ8, b),
The whole process can be written as:
Net(READ9, READ8, b) ?Row11Net(READ3, READ7,a) Net(READ7, READ1,
b)Net(READ1, READ8, b)
This will be a production in the CFG of the corresponding row language.
Question No: 33 ( Marks: 3 )
Find Pref (Q in R) for:
Q = {10, 11, 00, 010}
R = {01001, 10010, 0110, 10101, 01100, 001010}
Question No: 34 ( Marks: 5 )
Consider the Context Free Grammar (CFG)
S à 0AS | 0
A à S1A | SS | 1a
Show that the word 0000100 can be generated by this CFG by showing the whole
derivation starting from S
Question No: 35 ( Marks: 5 )
Consider the language L which is EVEN-EVEN, defined over Σ = {a,b}. In how many
classes does L may partition Σ*. Explain briefly.
Question No: 36 ( Marks: 5 )
What are the conditions (any five) that must be met to know that PDA is in
conversion form?
Ans:
Conversion form of PDA:
A PDA is in conversion form if it has following conditions:
1. The PDA must begin with the sequence
2. There is only one ACCEPT state.
3. Every edge leading out of any READ or HERE state goes directly into a POP
state.
4. There are no REJECT states.
5. All branching, deterministic or nondeterministic occurs at READ or HERE
states.
6. The STACK is never popped beneath this $ symbol.
7. No two POPs exist in a row on the same path without a READ or HERE.
8. Right before entering ACCEPT this symbol is popped out and left
/wEWBgL4j6fiAgK
MIDTERM EXAMINATION
Spring 2009
CS402- Theory of Automata (Session - 1)
Question No: 1 ( Marks: 1 ) - Please choose one
Alphabet S = {a,bc,cc} has _______ number of letters.
One
Two
Three
Four
Question No: 2 ( Marks: 1 ) - Please choose one
In which of the following language Rev(s)=s
EQUAL
INTEGER
PALINDROME
FACTORIAL
Question No: 3 ( Marks: 1 ) - Please choose one
If S = {ab, bb}, then S* will not contain
abbbab
bbba
bbbbab
ababbb
Question No: 4 ( Marks: 1 ) - Please choose one
a,b
1–
2+
a,b
Above given FA generates the language having strings of _________
ODD length
EVEN length
Equal number of a’s and b’s
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
a+b
a+b
aa+bb
+
Above given GTG accepts the language in which strings
Contains double a or double b
Contains both a and double b
Depends on the alphabet
None of these
Question No: 6 ( Marks: 1 ) - Please choose one
aa+bb
aa+bb
ab+ba
3- 2 1
ab+ba
4+
If above given TG is drawn like
aa+bb
31
X
4
+
Then what will be written in place of X.
(ab+ba)(aa+bb)(ba+ab)
(ab+ba)(aa+bb)(ab+ba)
(ab+ba)(aa+bb)*(ab+ba)
(ab+ba)(aa+bb)(ab+ba)*
Question No: 7 (Marks: 1) - Please choose one
FA3 expresses r1r2. Then initial state of FA3 will consist of
Initial state of FA2
Initial state of FA1
Initial states of both FA1 & FA2
Depends on FA’s
Question No: 8 ( Marks: 1 ) - Please choose one
FA3 expresses r1r2. Then there will be at least one final state of FA3 that consist
of final state of FA1 and initial state of FA2.
True
False
Depends on language
None of these
Question No: 9 ( Marks: 1 ) - Please choose one
Two machines are said to be equivalent if they print the same output string when
the different input string is run on them
True
False
Depends on language
May be or may not be
Question No: 10 ( Marks: 1 ) - Please choose one
Running the string abbabbba on this Moore machine. The outputs will
be________
b
q1/0 q2 /1
ab
a
q0/1 a
b
a
q3/1 1
b
b
a
2
q3 /0
101111010
01111010
01011110
01010101
Question No: 11 ( Marks: 1 ) - Please choose one
4a
2
a
a
a, b a, b
• 1 – 6+
� a,b
� a,b
o b
o b
aaa,bbb
b
5
3+
Above given TG’s are ______________.
None of these
Equivalent
Non-equivalent
TG’s are not valid
Question No: 12 ( Marks: 1 ) - Please choose one
TG can have more than one initial state.
True
False
Depends on alphabets
None of these
Question No: 13 ( Marks: 1 ) - Please choose one
a
a
+
––
a
b
b
b
Above given FA accepts null string.
True
False
FA is not valid
None of these
Question No: 14 ( Marks: 1 ) - Please choose one
If in an NFA, is allowed to be a label of an edge then that NFA is called
_________.
Will not remain NFA
NFA with
NFA with null string
Either "NFA with null string" OR "NFA with "
Question No: 15 ( Marks: 1 ) - Please choose one
One FA has n states and m letters in the alphabet. Then FA will have _____
number of transitions in the diagram.
(n)+(m)
(m)(n) OR (n)(m)
None of the given options
(m)-(n)
Question No: 16 ( Marks: 1 ) - Please choose one
(a+b)*a(a+b)*b(a+b)* is the RE of language defined over S={a,b} having at
least one a
and one b
True
False
Such a language does not exist
None of the given options
Question No: 17 ( Marks: 1 )
Is the following statement true?
A regular language can not be infinite.
Ans : If Regular language is infinite then RE is also infinite it depends on
language
Question No: 18 ( Marks: 1 )
Can you say that for a certain string there may be more than one paths in a TG?
Ans : TG there is only one certain path state but in GTG there is lot of states and
paths
Question No: 19 ( Marks: 2 )
If a language can be accepted by an FA then it can be accepted by a TG as well.
What are the other two statements of kleenes’s theorem?
Ans : TG and FA are same but TG is also considered as FA and FA is also
Considered as a TG as well
Question No: 20 (Marks: 3 )
Describe the method of NFA corresponding to Concatenation of FAs.
Ans : NFA build with FA there is TWO FA concatenate with each other and
some useless
state can be eliminate then NFA
Question No: 21 ( Marks: 5 )
Draw FA corresponding to following NFA?
2
b
a
1- 4+
a
b
3
Question No: 22 ( Marks: 10 )
Let L be any language. Let us define the transpose of L to be the language of
exactly
those words that are the words in L spelled backward. If w L then reverse (w)
L. for
example, if L = {a, abb, bbaab, bbbaa}Then Transpose (L) = {a, bba, baabb,
aabbb,
Prove that if there is an FA that accepts L, then there is a TG that accepts the
transpose of
L.
Automata
_______________are conventional names of the command line
parameters of
the ‘main()’ function.
Select correct option:
1. ‘argb’ and ‘argv’
2. ‘argc’ and ‘argv’
3. ‘argc’ and ‘argu’
4. None of the given
In_________, we try to have a precise problem statement
Select correct option:
1. Analysis
2. Design
3. Coding
4. None of the given
Pointers are a special type of __________in which a memory address is
stored
Select correct option:
1. variables
2. Location
3. Characters
4. None
of the given
At the design phase, we try to break up the problem into___________
Select correct option:
1. functional units
2. non-functional units
3. small units
4. None of the given
char name [] = “Hello World” ; In the above statement, a memory of
_________
characters will be allocated
Select correct option:
1. 13
2. 11
3. 12
4. 10
Pointers work by pointing to a particular___________
Select correct option:
1. Value
2. variable
3. data type(doubtful)
4. None of the given
___________ Returns true if c is a digit and false otherwise.
Select correct option:
1. int isalpha( int c )
2. int isalnum( int c )
3. int isxdigit( int c )
4. int isdigit( int c )
The ASCHI code of null character is___________
Select correct option:
1. 000
2. 010
3. 111
4. 110
The increment of a pointer depends on its___________.
Select correct option:
1. variable
2. value
3. data type
4. None of the given
At the___________, we try to break up the problem into functional units
Select correct option:
1. analysis phase
2. design phase
3. Implementation phase
4. None
of the given
To get the value stored at a memory address, we use
the________________
Select correct option:
1. referencing operator
2. dereferencing operator
3. simple operator
4. None of the given
suppose we have int y[10]; To access the 4th element of the array we
write_________
Select correct option:
1. y[4];
2. y[3];
3. y[2];
4. none of given
A character is stored in the memory in _________
Select correct option:
1. byte
2. integer
3. string
4. None of the given
QNo1.What is the difference between the strings and the words of a language?
A string is any combination of the letters of an alphabet where as the words of a
language are the strings that are always made according to certain rules used to
define that language.
For example if we take
Alphabet Σ = { a , b }
Here a , b are the letters of this alphabet.
As you can see we can make a lot of strings from these letters a and b.
For example
a,b,aa,ab,ba,bb,aaa,aab,aba,baa,............................................................ and so
on.
But when we define a language over this alphabet having no a's and only odd
number of b's.
Then the words of this language would have only those strings that have only odd
number of b's and no a's.
some example words of our defined language are
b , bbb , bbbbb , bbbbbbb ,...................................and so on.
So we can say that all the words are strings but all the strings may not be the
words of a language.
So strings are any combination of letters of an alphabet and the words of a
language are strings made according to some rule.
QNo.2 What is the difference between an Alphabet and an element of a
set. Whether Alphabet is an element of a set or it is a set itself?
An Alphabet is a set in itself. The elements of an Alphabet are called letters .
For example
Binary Alphabet Σ = {0,1}
Here 0,1 are the letters of binary alphabet.
Binary Alphabet is very important because it the Alphabet used by the computer.
Set of Natural Numbers
N={1,2,3,4,5,.........................................}
Here 1,2,3........................................... are the elements of set of Natural
Numbers.
QNo.3 What is Null String (Λ) ?
The string with zero occurrences of symbols (letters) from Σ.
It is denoted by (Small Greek letter Lambda) λ or (Capital Greek letter
Lambda) Λ, is called an empty string or null string.
The capital lambda will mostly be used to denote the empty string, in further
discussion.
QNo.4 What is PALINDROME ?
The language consisting of Λ (Null String) and the strings s defined over an
Alphabet Σ such that
Rev(s)=s.
Some example words of this language are
aa
As Rev(aa) = aa
aba
As Rev(aba) = aba
bbb
As Rev(bbb) = bbb
aabaa
As Rev(aabaa) = aabaa
bbbaaabbb
As Rev( bbbaaabbb ) = bbbaaabbb
It is to be noted that the words of PALINDROME are called palindromes.
QNo5.What is the concept of valid and invalid alphabets ?
While defining an alphabet of letters consisting of more than one symbols, no
letter should be started with any other the letter of the same alphabet i.e. one
letter should not be the prefix of another. However, a letter may be ended in the
letter of same alphabet i.e. one letter may be the suffix of another.
Σ= { a , b } ( Valid Alphabet)
Σ= { a , b , cd } ( Valid Alphabet)
Σ= { a , b , ac } ( Invalid Alphabet)
QNo 6. What is ALGOL ?
ALGOL (ALGOrithmic Language) is one of several high level languages designed
specifically for programming scientific computations. It started out in the late
1950's, first formalized in a report titled ALGOL 58, and then progressed through
reports ALGOL 60, and ALGOL 68. It was designed by an international
committee to be a universal language. Their original conference, which took
place in Zurich, was one of the first formal attempts to address the issue of
software portability. ALGOL's machine independence permitted the designers to
be more creative, but it made implementation much more difficult. Although
ALGOL never reached the level of commercial popularity of FORTRAN and
COBOL, it is considered the most important language of its era in terms of its
influence on later language development. ALGOL’s lexical and syntactic
structures became so popular that virtually all languages designed since have
been referred to as "ALGOL - like"; that is they have been hierarchical in
structure with nesting of both environments and control structures.
QNo 8.What is Non-Determinism and Determinism and what is the difference
between them ?
Determinism means that our computational model (machine) knows what to do
for every possible inputs. Non determinism our machine may or may not know
what it has to do on all possible inputs.
As you can conclude from above definition that Non-Deterministic machine can
not be implemented ( used ) on computer unless it is converted in Deterministic
machine.
QNo 9. What is meant by equivalent FA's ?
FA's that accept the same set of languages are called Equivalent FA's.
QNo11.Define Kleene Star?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the
collection of all strings defined over Σ, including Λ
It is to be noted that Kleene Star Closure can be defined over any set of strings.
Examples
If Σ = {x}
Then Σ* = {Λ, x, xx, xxx, xxxx, ….}
If Σ = {0,1}
Then Σ* = {Λ, 0, 1, 00, 01, 10, 11, ….}
If Σ = {aaB, c}
Then Σ* = {Λ, aaB, c, aaBaaB, aaBc, caaB, cc, ….}
Note:
Languages generated by Kleene Star Closure of set of strings, are infinite
languages. (By infinite language, it is supposed that the language contains infinite
many words, each of finite length)
QNo12.Valid/In-Valid alphabets?
Any alphabet is valid if any of its letter does not appear in the start of any other
letter otherwise it is invalid.
QNo13.What is Reverse of a string?
Alphabet provides only a set of symbols. A string is a concatenation of these
symbols. Reverse of the string means to write the string in reverse order. It has
no effect on alphabet. Alphabet will remain same.
QNo14.Differentiate Kleene Star Closure and PLUS?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the
collection of all strings defined over Σ, including Λ.
Plus Operation is same as Kleene Star Closure except that it does not generate
Λ (null string), automatically.
You can use other symbol for alphabet but we are mostly use sigma symbol.
QNo15.Define Regular Expression?
Regular Expression is the generalized form of any regular language through
which you can construct any string related to that language.
Take an example from your handouts
L1 = {Λ, a, aa, aaa, …} and L2 = {a, aa, aaa, aaaa, …} can simply be expressed
by a* and a+, respectively.
so a* and a+ are the generalized form of Languages L1, L2.
And a* and a+ are called the regular expressions (RE) for L1 and L2 respectively.
Bottom of Form
Bottom of Form
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Bottom of Form
Bottom of Form
Time Left 90
sec(s)
Question # 10 of 10 ( Start time: 10:38:00
PM )
Total Marks:
1
The input string is placed, before it runs, in
Select correct option:
Stack
Memory
Tape
Ram
Question # 4 of 10 ( Start time: 10:32:44 PM
)
Total Marks:
1
In CFG, the symbols that cannot be replaced by anything are
called
Select correct option:
Terminals
Non terminals
Productions
None of the given options
Quiz Start Time: 10:30 PM
Time Left 90
sec(s)
Question # 2 of 10 ( Start time: 10:31:15 PM
)
Total Marks:
1
If L1 and L2 are regular languages then which statement is
NOT true?
Select correct option:
L1 + L2 is always regular
L1 L2 is always regular
L1/L2 is always regular
L1* is always regular
Time Left 90
sec(s)
Question # 3 of 10 ( Start time: 10:31:31 PM
) Total Marks: 1
uced all the strings of a language is called
Select correct option:
Derivation tree
Ambiguous tree
Total language tree
Non ambiguous tree
Question # 8 of 10 ( Start time:
10:35:28 PM ) Total Marks: 1
The part of an FA, where the input string is placed before it is run, is
called _______
Select correct option:
State
Transition
Input Tape
Output Tape
Question # 1 of 10 ( Start time:
10:30:58 PM ) Total Marks: 1
By removing null and unit productions:
Select correct option:
CNF can be converted into CFG
CFG can be converted into CNF
CNF can be converted into TG
None of the given options
QNo1.What is the difference between the strings and the words of a language?
A string is any combination of the letters of an alphabet where as the words of a language
are the strings that are always made according to certain rules used to define that
language.
For example if we take
Alphabet Σ = { a , b }
Here a , b are the letters of this alphabet.
As you can see we can make a lot of strings from these letters a and b.
For example
a,b,aa,ab,ba,bb,aaa,aab,aba,baa,............................................................ and so on.
But when we define a language over this alphabet having no a's and only odd number
of b's.
Then the words of this language would have only those strings that have only odd number
of b's and no a's.
some example words of our defined language are
b , bbb , bbbbb , bbbbbbb ,...................................and so on.
So we can say that all the words are strings but all the strings may not be the words of a
language.
So strings are any combination of letters of an alphabet and the words of a language are
strings made according to some rule.
QNo.2 What is the difference between an Alphabet and an element of a set. Whether
Alphabet is an element of a set or it is a set itself?
An Alphabet is a set in itself. The elements of an Alphabet are called letters .
For example
Binary Alphabet Σ = {0,1}
Here 0,1 are the letters of binary alphabet.
Binary Alphabet is very important because it the Alphabet used by the computer.
Set of Natural Numbers
N={1,2,3,4,5,.........................................}
Here 1,2,3........................................... are the elements of set of Natural Numbers.
QNo.3 What is Null String (Λ) ?
The string with zero occurrences of symbols (letters) from Σ.
It is denoted by (Small Greek letter Lambda) λ or (Capital Greek letter Lambda) Λ, is called
an empty string or null string.
The capital lambda will mostly be used to denote the empty string, in further discussion.
QNo.4 What is PALINDROME ?
The language consisting of Λ (Null String) and the strings s defined over an Alphabet Σ
such that
Rev(s)=s.
Some example words of this language are
aa
As Rev(aa) = aa
aba
As Rev(aba) = aba
bbb
As Rev(bbb) = bbb
aabaa
As Rev(aabaa) = aabaa
bbbaaabbb
As Rev( bbbaaabbb ) = bbbaaabbb
It is to be noted that the words of PALINDROME are called palindromes.
QNo5.What is the concept of valid and invalid alphabets ?
While defining an alphabet of letters consisting of more than one symbols, no letter should
be started with any other the letter of the same alphabet i.e. one letter should not be the
prefix of another. However, a letter may be ended in the letter of same alphabet i.e. one
letter may be the suffix of another.
Σ= { a , b } ( Valid Alphabet)
Σ= { a , b , cd } ( Valid Alphabet)
Σ= { a , b , ac } ( Invalid Alphabet)
QNo 6. What is ALGOL ?
ALGOL (ALGOrithmic Language) is one of several high level languages designed
specifically for programming scientific computations. It started out in the late 1950's, first
formalized in a report titled ALGOL 58, and then progressed through reports ALGOL 60,
and ALGOL 68. It was designed by an international committee to be a universal language.
Their original conference, which took place in Zurich, was one of the first formal attempts to
address the issue of software portability. ALGOL's machine independence permitted the
designers to be more creative, but it made implementation much more difficult. Although
ALGOL never reached the level of commercial popularity of FORTRAN and COBOL, it is
considered the most important language of its era in terms of its influence on later language
development. ALGOL’s lexical and syntactic structures became so popular that virtually all
languages designed since have been referred to as "ALGOL - like"; that is they have been
hierarchical in structure with nesting of both environments and control structures.
QNo7. What are the Sequential Operators?
Sequencing Operators:
Sequencing operators
a >> b Sequence Match a and b in sequence
a && b Sequential-and Sequential-and. Same as above, match a
and b in sequence
a || b Sequential-or Match a or b in sequence
The sequencing operator >> can alternatively be thought of as the sequential-and operator.
The expression a && b reads as match a and b in sequence. Continuing this logic, we can
also have a sequential-or operator where the expression a || b reads as match a or b and in
sequence. That is, if both a and b match, it must be in sequence; this is equivalent to a >> !b
| b.
QNo 8.What is Non-Determinism and Determinism and what is the difference between
them ?
Determinism means that our computational model (machine) knows what to do for every
possible inputs. Non determinism our machine may or may not know what it has to do on all
possible inputs.
As you can conclude from above definition that Non-Deterministic machine can not be
implemented ( used ) on computer unless it is converted in Deterministic machine.
QNo 9. What is meant by equivalent FA's ?
FA's that accept the same set of languages are called Equivalent FA's.
QNo 10. What is the difference between Palindrome and Reverse function?
It is to be denoted that the words of PALINDROME are called palindromes.
Reverse (w) = w
Example: Σ={a,b},
PALINDROME={Λ , a, b, aa, bb, aaa, aba, bab, bbb, ...}
If a is a word in some language L, then reverse (a) is the same string of letters spelled
backwards, called the reverse of a.
e.g
reverse (xxx) = xxx
reverse (623) = 326
reverse (140) = 041
QNo11.Define Kleene Star?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the collection of
all strings defined over Σ, including Λ
It is to be noted that Kleene Star Closure can be defined over any set of strings.
Examples
If Σ = {x}
Then Σ* = {Λ, x, xx, xxx, xxxx, ….}
If Σ = {0,1}
Then Σ* = {Λ, 0, 1, 00, 01, 10, 11, ….}
If Σ = {aaB, c}
Then Σ* = {Λ, aaB, c, aaBaaB, aaBc, caaB, cc, ….}
Note:
Languages generated by Kleene Star Closure of set of strings, are infinite languages. (By
infinite language, it is supposed that the language contains infinite many words, each of
finite length)
QNo12.Valid/In-Valid alphabets?
Any alphabet is valid if any of its letter does not appear in the start of any other letter
otherwise it is invalid.
QNo13.What is Reverse of a string?
Alphabet provides only a set of symbols. A string is a concatenation of these symbols.
Reverse of the string means to write the string in reverse order. It has no effect on alphabet.
Alphabet will remain same.
QNo14.Differentiate Kleene Star Closure and PLUS?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the collection of
all strings defined over Σ, including Λ.
Plus Operation is same as Kleene Star Closure except that it does not generate Λ (null
string), automatically.
You can use other symbol for alphabet but we are mostly use sigma symbol.
QNo15.Define Regular Expression?
Regular Expression is the generalized form of any regular language through which you can
construct any string related to that language.
Take an example from your handouts
L1 = {Λ, a, aa, aaa, …} and L2 = {a, aa, aaa, aaaa, …} can simply be expressed by a * and
a+, respectively.
so a* and a+ are the generalized form of Languages L1, L2.
And a* and a+ are called the regular expressions (RE) for L1 and L2 respectively.
Q No.1 What is the concept of FA also known as FSM ( Finite State Machine) ?
FA (Finite Automaton) is a finite state machine that recognizes a regular language. In
computer science, a finite-state machine (FSM) or finite-state automaton (FSA) is an
abstract machine that has only a finite, constant amount of memory. The internal states of
the machine carry no further structure. This kind of model is very widely used in the study of
computation and languages.
Q No.2 What is the difference between FA , TG , GTG. ?
In FA we mark transitions with single letter of the given alphabet but in TG transitions can
be marked with letters or strings ( combination of letters).
In every FA, every state shows transition for all letters of given alphabet but in any TG it is
not necessary to show all transition for all letters of given alphabet. In TG, we may or may
not show all letter transitions according to requirement. We can also show transitions on
reading any strings in TGs but it is not possible in FA's. In GTG Directed edges connecting
some pair of states are labeled with regular expressions . It may be noted that in GTG, the
labels of transition edges are corresponding regular expressions. In TG we write strings and
in GTG we are bound to write RE. Every FA is also a TG but not every TG is FA.
Q No.3 What is the difference between FA's and TG's .Why we need TG's when we have
FA's?
The Transition Graphs (TG) differ from FA in the following areas
TG's are generalizations of FA's.
TG's can change state without an input ( Null transition).
Can read more than one letter (words of the language they are accepting ) along the
transition edges at a time.
Can have a regular expression as a edge label.
Can have more then one start state.
We have been given more freedom in TG's. But this freedom is on the cost of more memory
and processing power it means that if we implement TG's on computer using some
programming language it will need more memory and processing power of computer than
used in the implementation of FA's.
Q No.4 What is the concept of the Union of FA's ?
When we take Union of two FA's it means that resultant FA's should accept all the words
that were accepted by the two FA's individually. It is like taking union of two sets, the
resultant set contain members of both sets.
For example
Let A ={1,3,5,7,9}
and
B = {0,2,4,6,8,10}
then, A U B = { 0,1,2,3,4,5,6,7,8,9,10 }
you can see that A U B contain elements of both sets similar is the case with FA's.
Q No.5 What is the difference between is TG and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
Q No.6 How one can create RE of a particular language?
First thing about RE and FA is that there is no hard and fast formula or method to generate
these. One can generate them by its mental approach. And this mental approach can be
acquired through only PRACTICE.
Here are some useful tips to write RE's,
If we have a finite language( language having countable words ) then its RE will not have *
in it
e.g.
Let our language consist of the words of length three exactly over alphabet Σ= {a,b}
then it consists of the words
L = {aaa, aab, aba,abb,baa,bab,bba,bbb}.
Its RE can be simply written as
RE = aaa + aab + aba + abb + baa + bab + bba + bbb
which simply means that our language consists of only these words.
So we can make RE for a finite language by writing its all words with + operator between
them.
If we have an infinite language, then there will be * in it’s RE.
We should also keep the null string in our mind. If our language generates null string than
our RE should also generate it)
For example language having all the words of even length has null string in it as well so we
can write its RE as follows
RE = ((a+b)(a+b))*
This RE also generates null string.
If a language generates all strings starting with a. then strings will be of type
a , aa, ab, aab, aaa, aba, abb,….
Here RE should start with ‘a’ and then all strings including null. So this will be (a + b)* and
complete RE is a (a+ b)*.
Similarly languages of strings ending in b will have RE (a + b)*b.
Q No.7 What is the diagrammatically difference between FA's and TG's?
The main differences between FA’s and TG’s are as follows
•
In FA there can be maximum one initial or starting state while in TG there may be
more than one initial state.
• In FA there can be transition for letters only while in TG transitions can be marked
with letters or strings as well.
• In FA there must be transition from each state for each letter (deterministic) while in
TG there may be no transition for specific letter from a state and there may be more
than one path for a string or letter from a state.
Q No.8 What is the corresponding FA for RE =aa((a+b)(a+b))*
RE is aa((a + b)(a + b))*. Its corresponding FA is as follows.
Q No.9 What is difference between FA's and NFA's. Are they opposite to each other ?
FA stands for finite automata while NFA stands for non-deterministic finite automata
In FA there must be a transition for each letter of the alphabet from each state. So in FA
number of transitions must be equal to (number of states * number of letter in alphabet).
While in NFA there may be a transition for a letter from a state. In NFA there may be more
than one transition for a letter from a state. And finally every FA is an NFA while every NFA
may be an FA or not.
Q No.10 Differentiate between (a,b) and (a+b)?
(a, b) = Represents a and b.
(a + b) = Represents either a or b.
Q No.1 What is the difference between how’s FA and TG .Why we need TG's when we
have FA's?
The Transition Graphs (TG) differ from FA in the following areas
TG's are generalizations of FA's.
TG's can change state without an input ( Null transition).
Can read more than one letter (words of the language they are accepting ) along the
transition edges at a time.
Can have a regular expression as a edge label.
Can have more then one start state.
We have been given more freedom in TG's. But this freedom is on the cost of more memory
and processing power it means that if we implement TG's on computer using some
programming language it will need more memory and processing power of computer than
used in the implementation of FA's.
Q No.2 What is the concept of the Union of FA's ?
When we take Union of two FA's it means that resultant FA's should accept all the words
that were accepted by the two FA's individually. It is like taking union of two sets the
resultant set contain members of both sets.
For example
Let A ={1,3,5,7,9}
and
B = {0,2,4,6,8,10}
then, A U B = { 0,1,2,3,4,5,6,7,8,9,10 }
you can see that A U B contain elements of both sets similar is the case with FA's.
Q No.3 What is the difference between GT and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
Q No.4 How to create a RE of a particular Language?
Regular expression is used to express the infinite or finite language, these RE are made in
such a way that these can generate the strings of that unique language also for the cross
check that the defined RE is of a specified language that RE should accept all the string of
that language and all language strings should be accepted by that RE.
Q No.5 How diagrams of FA's are created ?
It depends upon the question how many states involve in a FA. There is not any formal
procedure to design FA for a language. This ability just improves with time and practice.
Every FA is also a TG but not every TG is FA. In every FA, every state shows transition of
all letters of given alphabet but in any TG it is not must. In TG, we may or may not show all
letters transition according to requirement. We can also show transitions on reading any
strings in TGs but it is not possible in FAs.
Q No.6 How one can create RE of a particular language?
First thing about RE and FA is that there is no hard and fast formula or method to generate
these. One can generate them by their mental approach. And this mental approach can be
acquired through only PRACTICE.
I am giving you few tips. I hope those will help you.
If we have a finite language then it will always be regular and will not have * in RE.
e.g. L={aaa, aba, bb}. L language generates given three strings then its RE will be
(aaa + aba + bb}. So in finite language + of all strings can be it’s RE.
If we have an infinite language, then there will be * in it’s RE.
We should also keep the null string in our mind.
For practice just try to create RE of simple languages. Don’t try to confuse yourself with
complex languages.
For example if a language generates all strings starting with a. then strings will be of type
a , aa, ab, aab, aaa, aba, abb,….
Here RE should start with ‘a’ and then all strings including null. So this will be (a + b)* and
complete RE is a (a+ b)*.
Similarly languages of strings ending in b will have RE (a + b)*b.
I hope now you will be able to generate the RE of simpler languages. Gradually, increase
the complexity of languages to become a perfect in RE’s.
Now as similar to RE, FA of finite language will not have any loop in it.
If language is infinite then there will always be at least one loop in its FA.
From RE, if you want to generate its FA, then first get the smallest strings and generate
their FA and then gradually get the strings of bigger length and keep amending the created
FA. After some practice, you will be able to generate the FA’s.
And the last thing nobody can do the new task accurately for the first time. Practice is the
key to success. In the start you will have lot of mistakes but after practice you will be able to
clear all of them.
Q No.7 What is the difference between FA's ,and TG's ?
There are two or three big differences between FA’s and TG’s.
In FA there can be maximum one initial or starting state while in TG there may be more
than one initial state.
In FA there can be transition for letters only while in TG transitions from a state to another
one can be for strings.
In FA there must be transition from each state for each letter (deterministic) while in TG
there may be no transition for specific letter from a state and there may be more than one
path for a string or letter from a state.
Q No.8 What is the exact definition of FA ?
Definition:
A Finite automaton (FA), is a collection of the followings
Finite number of states, having one initial and some (maybe none) final states.
Finite set of input letters (Ó) from which input strings are formed.
Finite set of transitions i.e. for each state and for each input letter there is a transition
showing how to move from one state to another.
Q No.9 What is the difference between TG and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
For RE =aa((a+b)(a+b))* what will be its corresponding FA ?
RE is aa((a + b)(a + b))*. Its corresponding FA is as follows.
Q No.10 What is the difference between FA and NFA ?
FA stands for finite automata while NFA stands for non-deterministic finite automata
In FA there must be a transition for each letter of the alphabet from each state. So in FA
number of transitions must be equal to (number of states * number of letter in alphabet).
While in NFA there may be a transition for a letter from a state. In NFA there may be more
than one transition for a letter from a state. And finally every FA is an NFA while every NFA
may be an FA.
FA:
NFA:
Q No.11 What is the method to understanding FA's and NFA's
Firstly we know that an FA is used to describe a language. Now a language consists of
strings. FA will describe the specific language only if it accepts all the strings of that
particular language and all the strings generated by the FA are in the language. So
confirmation is of two ways.
Now, how to traverse the FA. It is very easy. Every FA has one initial state (state with sign). From every state of FA there is one transition for every letter of the alphabet. Read
the string letter by letter and move according to transitions from state to state. If the string
ends in the final state (state with a + sign), that particular string will be accepted otherwise
rejected.
So, every string ending in final state will be accepted by FA and will be a word of the
language.
For NFA, there may be no path or more than one path for a letter from a specific state. As
similar to FA just start traversing from the initial state and if the string ends in the final state,
it will be accepted.
Remember, as there may be more than one path for a letter from a state. So any path can
be used. Goal is to reach the final state. Remaining theory is same to the FA.
Practice is the key to success. Just try simple FA's and NFA's in the start.
Q No 1.What is the concept of Nondeterministic Finite Automaton (NFA) ?
Nondeterminism plays a key role in the theory of computing. A nondeterministic finite state
automaton is one in which the current state of the machine and the current input do not
uniquely determine the next state. This just means that a number of subsequent states
(zero or more) are possible next states of the automaton at every step of a computation.
Of course, nondeterminism is not realistic, because in real life, computers must be
deterministic. Still, we can simulate nondeterminism with deterministic programs.
Furthermore, as a mathematical tool for understanding computability, nondeterminism is
invaluable.
As with deterministic finite state automata, a nondeterministic finite state automaton has
five components.
1. a set of states
2. a finite input alphabet from which input strings can be constructed
3. a transition function that describes how the automaton changes states as it
processes an input string
4. a single designated starting state
5. a set of accepting states
The only difference lies in the transition function, which can now target subsets of the states
of the automaton rather than a single next state for each state, input pair.
Q No 2. If a language can be expressed in the form of FA than why it is needed to use NFA
?
NFA stands for non-deterministic FA and this sort of structure has relaxation compared with
FA. So it is rather more easy to represent a language using NFA.
We have methods to convert NFA into FA's so sometimes it is easier to build NFA of a
given language and than convert its NFA into FA using these methods rather than directly
building an FA for a language which may be very difficult.
Q No 3.How to made NFA corresponding to the closure of an FA ?
While generating NFA corresponding to closure of an FA one should take care of the null
string. Simple way to accept null string is declare initial state, final as well. But in this way a
lot of other strings will also be accepted. Therefore, accurate way is draw another state.
Declare the new state initial as well as final. Connect the new state with the states originally
connected with the old start state with the same transitions as the old start state. Newly
drawn diagram will be an NFA representing the language closure of the given FA
Q No 4.What is the difference between Union of two FA’s , Concatenation of two FA’s and
closure of two FA’s ?
Consider two FA's given below
Here FA1 accepts all strings ending in a and FA2 accepts all strings ending b.
An FA corresponding to FA1UFA2 will accept all the strings ending in a or ending in b. for
example, aba,bbaaab,bbb
An FA corresponding to FA1FA2 will accept all the strings whose first substring belongs to
FA1 and second substring belongs to FA2. for example, ababab, bbabbb.
An FA corresponding to FA1* will accepts all the strings of FA1 including null string. if FA1
represents RE r1 then FA1* will correspond to RE r1*.
(NFA) : An NFA is a TG with a unique start state and a property of having single letter
as label of transitions. An NFA is a collection of three things
1) Finite many states with one initial and some final states
2) Finite set of input letters, say, S = {a, b, c}
3) Finite set of transitions, showing where to move if a letter is input at
certain state (Ù is not a valid transition), there may be more than one
transition for certain letters and there may not be any transition for certain
letters.
A Mealy machine consists of the following
1. A finite set of states q0, q1, q2, … where q0 is the initial state.
2. An alphabet of letters _ = {a,b,c,…} from which the input strings are formed.
3. An alphabet G={x,y,z,…} of output characters from which output strings are
generated.
4. A pictorial representation with states and directed edges labeled by an input letter
along with an output character. The directed edges also show how to go from one state
to another corresponding to every possible input letter.
(It is not possible to give transition table in this case.)
Note
It is to be noted that since, similar to Moore machine, in Mealy machine no state is
designated to be a final state, so there is no question of accepting any language by Mealy
machine. However in some cases the relation between an input string and the
corresponding output string may be identified by the Mealy machine. Moreover, the state to
be initial is not important as if the machine is used several times and is restarted after some
time, the machine will be started from the state where it was left off.
Automata Theory by
Muhammad Ishfaq
FAQ's about Lectures 1 to 5
QNo1.What is the difference between the strings and the words of a language?
QNo.2 What is the difference between an Alphabet and an element of a set . Whether
Alphabet is an
element of a set or it is a set itself ?
QNo.3 What is Null String (Λ) ?
QNo.4 What is PALINDROME ?
QNo5.What is the concept of valid and invalid alphabets ?
QNo 6. What is ALGOL ?
QNo7. What are the Sequential Operators?
QNo 8.What is Non-Determinism and Determinism and what is the difference between
them ?
QNo 9. What is meant by equivalent FA's ?
QNo 10. What is the difference between Palindrome and Reverse function?
QNo11.Define Kleene Star?
QNo12.Valid/In-Valid alphabets?
QNo13.What is Reverse of a string?
QNo14.Differentiate Kleene Star Closure and PLUS?
QNo15.Define Regular Expression?
QNo1.What is the difference between the strings and the words of a language?
A string is any combination of the letters of an alphabet where as the words of a language are
the
strings that
are always made according to certain rules used to define that language.
For example if we take
Alphabet Σ = { a , b }
Here a , b are the letters of this alphabet.
As you can see we can make a lot of strings from these letters a and b.
For example
a,b,aa,ab,ba,bb,aaa,aab,aba,baa,............................................................ and so on.
But when we define a language over this alphabet having no a's and only odd number of b's.
Then the words of this language would have only those strings that have only odd number of
b's
and no a's.
some example words of our defined language are
b , bbb , bbbbb , bbbbbbb ,...................................and so on.
So we can say that all the words are strings but all the strings may not be the words of a
language.
So strings are any combination of letters of an alphabet and the words of a language are
strings made
according to some rule.
QNo.2 What is the difference between an Alphabet and an element of a set. Whether
Alphabet is an
element of a set or it is a set itself?
An Alphabet is a set in itself. The elements of an Alphabet are called letters .
For example
Binary Alphabet Σ = {0,1}
Here 0,1 are the letters of binary alphabet.
Binary Alphabet is very important because it the Alphabet used by the computer.
Set of Natural Numbers
N={1,2,3,4,5,.........................................}
Here 1,2,3........................................... are the elements of set of Natural Numbers.
QNo.3 What is Null String (Λ) ?
The string with zero occurrences of symbols (letters) from Σ.
It is denoted by (Small Greek letter Lambda) λ or (Capital Greek letter Lambda) Λ, is called an empty
string
or null
string.
The capital lambda will mostly be used to denote the empty string, in further discussion.
QNo.4 What is PALINDROME ?
The language consisting of Λ (Null String) and the strings s defined over an Alphabet Σ such
that
Rev(s)=s.
Some example words of this language are
aa
As Rev(aa) = aa
aba
As Rev(aba) = aba
bbb
As Rev(bbb) = bbb
aabaa
As Rev(aabaa) = aabaa
bbbaaabbb
As Rev( bbbaaabbb ) = bbbaaabbb
It is to be noted that the words of PALINDROME are called palindromes.
QNo5.What is the concept of valid and invalid alphabets ?
While defining an alphabet of letters consisting of more than one symbols, no letter should be
started
with
any other the letter of the same alphabet i.e. one letter should not be the prefix of another.
However,
a letter
may be ended in the letter of same alphabet i.e. one letter may be the suffix of another.
Σ= { a , b } ( Valid Alphabet)
Σ= { a , b , cd } ( Valid Alphabet)
Σ= { a , b , ac } ( Invalid Alphabet)
QNo 6. What is ALGOL ?
ALGOL (ALGOrithmic Language) is one of several high level languages designed
specifically for
programming scientific computations. It started out in the late 1950's, first formalized in a
report
titled
ALGOL 58, and then progressed through reports ALGOL 60, and ALGOL 68. It was
designed by an
international committee to be a universal language. Their original conference, which took
place in
Zurich,
was one of the first formal attempts to address the issue of software portability. ALGOL's
machine
independence permitted the designers to be more creative, but it made implementation much
more
difficult.
Although ALGOL never reached the level of commercial popularity of FORTRAN and
COBOL, it
is
considered the most important language of its era in terms of its influence on later language
development.
ALGOL‟s lexical and syntactic structures became so popular that virtually all languages
designed
since have
been referred to as "ALGOL - like"; that is they have been hierarchical in structure with
nesting of
both
environments and control structures.
QNo7. What are the Sequential Operators?
Sequencing Operators:
Sequencing operators
a >> b Sequence Match a and b in sequence
a && b Sequential-and
Sequential-and. Same as above, match a and b in
sequence
a || b Sequential-or Match a or b in sequence
The sequencing operator >> can alternatively be thought of as the sequential-and operator.
The
expression a
&& b reads as match a and b in sequence. Continuing this logic, we can also have a
sequential-or
operator
where the expression a || b reads as match a or b and in sequence. That is, if both a and b
match, it
must be
in sequence; this is equivalent to a >> !b | b.
QNo 8.What is Non-Determinism and Determinism and what is the difference between
them ?
Determinism means that our computational model (machine) knows what to do for every
possible
inputs.
Non determinism our machine may or may not know what it has to do on all possible inputs.
As you can conclude from above definition that Non-Deterministic machine can not be
implemented
( used )
on computer unless it is converted in Deterministic machine.
QNo 9. What is meant by equivalent FA's ?
FA's that accept the same set of languages are called Equivalent FA's.
QNo 10. What is the difference between Palindrome and Reverse function?
It is to be denoted that the words of PALINDROME are called palindromes.
Reverse (w) = w
Example: Σ={a,b},
PALINDROME={Λ , a, b, aa, bb, aaa, aba, bab, bbb, ...}
If a is a word in some language L, then reverse (a) is the same string of letters spelled
backwards,
called the
reverse of a.
e.g
reverse (xxx) = xxx
reverse (623) = 326
reverse (140) = 041
QNo11.Define Kleene Star?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the collection of
all
strings defined
over Σ, including Λ
It is to be noted that Kleene Star Closure can be defined over any set of strings.
Examples
If Σ = {x}
Then Σ* = {Λ, x, xx, xxx, xxxx, ….}
If Σ = {0,1}
Then Σ* = {Λ, 0, 1, 00, 01, 10, 11, ….}
If Σ = {aaB, c}
Then Σ* = {Λ, aaB, c, aaBaaB, aaBc, caaB, cc, ….}
Note:
Languages generated by Kleene Star Closure of set of strings, are infinite languages. (By
infinite
language, it
is supposed that the language contains infinite many words, each of finite length)
QNo12.Valid/In-Valid alphabets?
Any alphabet is valid if any of its letter does not appear in the start of any other letter
otherwise it is
invalid.
QNo13.What is Reverse of a string?
Alphabet provides only a set of symbols. A string is a concatenation of these symbols.
Reverse of the
string
means to write the string in reverse order. It has no effect on alphabet. Alphabet will remain
same.
QNo14.Differentiate Kleene Star Closure and PLUS?
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the collection of
all
strings defined
over Σ, including Λ.
Plus Operation is same as Kleene Star Closure except that it does not generate Λ (null string),
automatically.
You can use other symbol for alphabet but we are mostly use sigma symbol.
QNo15.Define Regular Expression?
Regular Expression is the generalized form of any regular language through which you can
construct
any
string related to that language.
Take an example from your handouts
L1 = {Λ, a, aa, aaa, …} and L2 = {a, aa, aaa, aaaa, …} can simply be expressed by a * and a+,
respectively.
so a* and a+ are the generalized form of Languages L1, L2.
And a* and a+ are called the regular expressions (RE) for L1 and L2 respectively.
Question: FAQ's about Lectures 6 to 10
Automata Theory FAQ's about
Lectures 6
to 10
Answer:
Q No.1 What is the concept of FA also known as FSM ( Finite State Machine) ?
Q No.2 What is the difference between FA , TG , GTG. ?
Q No.3 What is the difference between FA's and TG's .Why we need TG's when we
have FA's?
Q No.4 What is the concept of the Union of FA's ?
Q No.5 What is the difference between is TG and GTG ?
Q No.6 How one can create RE of a particular language?
Q No.7 What is the diagrammatically difference between FA's and TG's?
Q No.8 What is the corresponding FA for RE = aa((a+b)(a+b))*
Q No.9 What is difference between FA's and NFA's. Are they opposite to each other ?
Q No.10 Differentiate between (a,b) and (a+b)?
Q No.1 What is the concept of FA also known as FSM ( Finite State Machine) ?
FA (Finite Automaton) is a finite state machine that recognizes a regular language. In
computer science, a finite-state machine (FSM) or finite-state automaton (FSA) is an abstract
machine that has only a finite, constant amount of memory. The internal states of the
machine
carry no further structure. This kind of model is very widely used in the study of computation
and languages.
Q No.2 What is the difference between FA , TG , GTG. ?
In FA we mark transitions with single letter of the given alphabet but in TG transitions can be
marked with letters or strings ( combination of letters).
In every FA, every state shows transition for all letters of given alphabet but in any TG it is
not necessary to show all transition for all letters of given alphabet. In TG, we may or may
not show all letter transitions according to requirement. We can also show transitions on
reading any strings in TGs but it is not possible in FA's. In GTG Directed edges connecting
some pair of states are labeled with regular expressions . It may be noted that in GTG, the
labels of transition edges are corresponding regular expressions. In TG we write strings and
in GTG we are bound to write RE. Every FA is also a TG but not every TG is FA.
Q No.3 What is the difference between FA's and TG's .Why we need TG's when we
have FA's?
The Transition Graphs (TG) differ from FA in the following areas
TG's are generalizations of FA's.
TG's can change state without an input ( Null transition).
Can read more than one letter (words of the language they are accepting ) along the transition
edges at a time.
Can have a regular expression as a edge label.
Can have more then one start state.
We have been given more freedom in TG's. But this freedom is on the cost of more memory
and processing power it means that if we implement TG's on computer using some
programming language it will need more memory and processing power of computer than
used in the implementation of FA's.
Q No.4 What is the concept of the Union of FA's ?
When we take Union of two FA's it means that resultant FA's should accept all the words that
were accepted by the two FA's individually. It is like taking union of two sets, the resultant
set contain members of both sets.
For example
Let A ={1,3,5,7,9}
and
B = {0,2,4,6,8,10}
then, A U B = { 0,1,2,3,4,5,6,7,8,9,10 }
you can see that A U B contain elements of both sets similar is the case with FA's.
Q No.5 What is the difference between is TG and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
Q No.6 How one can create RE of a particular language?
First thing about RE and FA is that there is no hard and fast formula or method to generate
these. One can generate them by its mental approach. And this mental approach can be
acquired through only PRACTICE.
Here are some useful tips to write RE's,
If we have a finite language( language having countable words ) then its RE will not have *
in it
e.g.
Let our language consist of the words of length three exactly over alphabet Σ= {a,b}
then it consists of the words
L = {aaa, aab, aba,abb,baa,bab,bba,bbb}.
Its RE can be simply written as
RE = aaa + aab + aba + abb + baa + bab + bba + bbb
which simply means that our language consists of only these words.
So we can make RE for a finite language by writing its all words with + operator between
them.
If we have an infinite language, then there will be * in it‟s RE.
We should also keep the null string in our mind. If our language generates null string than our
RE should also generate it)
For example language having all the words of even length has null string in it as well so we
can write its RE as follows
RE = ((a+b)(a+b))*
This RE also generates null string.
If a language generates all strings starting with a. then strings will be of type
a , aa, ab, aab, aaa, aba, abb,….
Here RE should start with „a‟ and then all strings including null. So this will be (a + b)* and
complete RE is a (a+ b)*.
Similarly languages of strings ending in b will have RE (a + b)*b.
Q No.7 What is the diagrammatically difference between FA's and TG's?
The main differences between FA‟s and TG‟s are as follows
• In FA there can be maximum one initial or starting state while in TG there may be
more than one initial state.
• _____In FA there can be transition for letters only while in TG transitions can be marked
with letters or strings as well.
• In FA there must be transition from each state for each letter (deterministic) while in
TG there may be no transition for specific letter from a state and there may be more
than one path for a string or letter from a state.
Q No.8 What is the corresponding FA for RE =aa((a+b)(a+b))*
RE is aa((a + b)(a + b))*. Its corresponding FA is as follows.
Q No.9 What is difference between FA's and NFA's. Are they opposite to each other ?
FA stands for finite automata while NFA stands for non-deterministic finite automata
In FA there must be a transition for each letter of the alphabet from each state. So in FA
number of transitions must be equal to (number of states * number of letter in alphabet).
While in NFA there may be a transition for a letter from a state. In NFA there may be more
than one transition for a letter from a state. And finally every FA is an NFA while every NFA
may be an FA or not.
Q No.10 Differentiate between (a,b) and (a+b)?
(a, b) = Represents a and b.
(a + b) = Represents either a or b.
Question: FAQ's about Lectures 11 to 15
Automata Theory FAQ's about
Lectures
11 to 15
Answer:
Q No.1 What is the difference between how’s FA and TG .Why we need TG's when we
have FA's?
Q No.2 What is the concept of the Union of FA's ?
Q No.3 What is the difference between GT and GTG ?
Q No.4 How to create a RE of a particular Language?
Q No.5 How diagrams of FA's are created ?
Q No.6 How one can create RE of a particular language?
Q No.7 What is the difference between FA's ,and TG's ?
Q No.8 What is the exact definition of FA ?
Q No.9 What is the difference between TG and GTG ?
Q No.10 What is the difference between FA and NFA ?
Q No.11 What is the method to understanding FA's and NFA's?
Q No.1 What is the difference between how’s FA and TG .Why we need TG's when we
have FA's?
The Transition Graphs (TG) differ from FA in the following areas
TG's are generalizations of FA's.
TG's can change state without an input ( Null transition).
Can read more than one letter (words of the language they are accepting ) along the transition
edges at a time.
Can have a regular expression as a edge label.
Can have more then one start state.
We have been given more freedom in TG's. But this freedom is on the cost of more memory
and processing power it means that if we implement TG's on computer using some
programming language it will need more memory and processing power of computer than
used in the implementation of FA's.
Q No.2 What is the concept of the Union of FA's ?
When we take Union of two FA's it means that resultant FA's should accept all the words that
were accepted by the two FA's individually. It is like taking union of two sets the resultant set
contain members of both sets.
For example
Let A ={1,3,5,7,9}
and
B = {0,2,4,6,8,10}
then, A U B = { 0,1,2,3,4,5,6,7,8,9,10 }
you can see that A U B contain elements of both sets similar is the case with FA's.
Q No.3 What is the difference between GT and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
Q No.4 How to create a RE of a particular Language?
Regular expression is used to express the infinite or finite language, these RE are made in
such a way that these can generate the strings of that unique language also for the cross check
that the defined RE is of a specified language that RE should accept all the string of that
language and all language strings should be accepted by that RE.
Q No.5 How diagrams of FA's are created ?
It depends upon the question how many states involve in a FA. There is not any formal
procedure to design FA for a language. This ability just improves with time and practice.
Every FA is also a TG but not every TG is FA. In every FA, every state shows transition of
all letters of given alphabet but in any TG it is not must. In TG, we may or may not show all
letters transition according to requirement. We can also show transitions on reading any
strings in TGs but it is not possible in FAs.
Q No.6 How one can create RE of a particular language?
First thing about RE and FA is that there is no hard and fast formula or method to generate
these. One can generate them by their mental approach. And this mental approach can be
acquired through only PRACTICE.
I am giving you few tips. I hope those will help you.
If we have a finite language then it will always be regular and will not have * in RE.
e.g. L={aaa, aba, bb}. L language generates given three strings then its RE will be
(aaa + aba + bb}. So in finite language + of all strings can be it‟s RE.
If we have an infinite language, then there will be * in it‟s RE.
We should also keep the null string in our mind.
For practice just try to create RE of simple languages. Don‟t try to confuse yourself with
complex languages.
For example if a language generates all strings starting with a. then strings will be of type
a , aa, ab, aab, aaa, aba, abb,….
Here RE should start with „a‟ and then all strings including null. So this will be (a + b)* and
complete RE is a (a+ b)*.
Similarly languages of strings ending in b will have RE (a + b)*b.
I hope now you will be able to generate the RE of simpler languages. Gradually, increase the
complexity of languages to become a perfect in RE‟s.
Now as similar to RE, FA of finite language will not have any loop in it.
If language is infinite then there will always be at least one loop in its FA.
From RE, if you want to generate its FA, then first get the smallest strings and generate their
FA and then gradually get the strings of bigger length and keep amending the created FA.
After some practice, you will be able to generate the FA‟s.
And the last thing nobody can do the new task accurately for the first time. Practice is the key
to success. In the start you will have lot of mistakes but after practice you will be able to clear
all of them.
Q No.7 What is the difference between FA's ,and TG's ?
There are two or three big differences between FA‟s and TG‟s.
In FA there can be maximum one initial or starting state while in TG there may be more than
one initial state.
In FA there can be transition for letters only while in TG transitions from a state to another
one can be for strings.
In FA there must be transition from each state for each letter (deterministic) while in TG
there may be no transition for specific letter from a state and there may be more than one path
for a string or letter from a state.
Q No.8 What is the exact definition of FA ?
Definition:
A Finite automaton (FA), is a collection of the followings
Finite number of states, having one initial and some (maybe none) final states.
Finite set of input letters (Ó) from which input strings are formed.
Finite set of transitions i.e. for each state and for each input letter there is a transition
showing
how to move from one state to another.
Q No.9 What is the difference between TG and GTG ?
In TG, there are transitions for the strings. While in GTG, one can write whole RE as a
transition from one state to another one.
For RE =aa((a+b)(a+b))* what will be its corresponding FA ?
RE is aa((a + b)(a + b))*. Its corresponding FA is as follows.
Q No.10 What is the difference between FA and NFA ?
FA stands for finite automata while NFA stands for non-deterministic finite automata
In FA there must be a transition for each letter of the alphabet from each state. So in FA
number of transitions must be equal to (number of states * number of letter in alphabet).
While in NFA there may be a transition for a letter from a state. In NFA there may be more
than one transition for a letter from a state. And finally every FA is an NFA while every NFA
may be an FA.
FA:
NFA:
Q No.11 What is the method to understanding FA's and NFA's
Firstly we know that an FA is used to describe a language. Now a language consists of
strings. FA will describe the specific language only if it accepts all the strings of that
particular language and all the strings generated by the FA are in the language. So
confirmation is of two ways.
Now, how to traverse the FA. It is very easy. Every FA has one initial state (state with -sign).
From every state of FA there is one transition for every letter of the alphabet. Read the string
letter by letter and move according to transitions from state to state. If the string ends in the
final state (state with a + sign), that particular string will be accepted otherwise rejected.
So, every string ending in final state will be accepted by FA and will be a word of the
language.
For NFA, there may be no path or more than one path for a letter from a specific state. As
similar to FA just start traversing from the initial state and if the string ends in the final state,
it will be accepted.
Remember, as there may be more than one path for a letter from a state. So any path can be
used. Goal is to reach the final state. Remaining theory is same to the FA.
Practice is the key to success. Just try simple FA's and NFA's in the start.
Question: FAQ's about Lectures 16 to 20
Automata Theory FAQ's about
Lectures
16 to 20
Answer:
Q No 1. What is the concept of Nondeterministic Finite Automaton (NFA) ?
Q No 2. If a language can be expressed in the form of FA than why it is needed to use
NFA ?
Q No 3 .How to made NFA corresponding to the closure of an FA ?
Q No 4 .What is the difference between Union of two FA’s , Concatenation of two FA’s
and closure of two FA’s ?
Q No 1.What is the concept of Nondeterministic Finite Automaton (NFA) ?
Nondeterminism plays a key role in the theory of computing. A nondeterministic finite state
automaton is one in which the current state of the machine and the current input do not
uniquely determine the next state. This just means that a number of subsequent states (zero or
more) are possible next states of the automaton at every step of a computation.
Of course, nondeterminism is not realistic, because in real life, computers must be
deterministic. Still, we can simulate nondeterminism with deterministic programs.
Furthermore, as a mathematical tool for understanding computability, nondeterminism is
invaluable.
As with deterministic finite state automata, a nondeterministic finite state automaton has five
components.
1. a set of states
2. a finite input alphabet from which input strings can be constructed
3. a transition function that describes how the automaton changes states as it processes
an input string
4. a single designated starting state
5. a set of accepting states
The only difference lies in the transition function, which can now target subsets of the states
of the automaton rather than a single next state for each state, input pair.
Q No 2. If a language can be expressed in the form of FA than why it is needed to use
NFA ?
NFA stands for non-deterministic FA and this sort of structure has relaxation compared with
FA. So it is rather more easy to represent a language using NFA.
We have methods to convert NFA into FA's so sometimes it is easier to build NFA of a given
language and than convert its NFA into FA using these methods rather than directly building
an FA for a language which may be very difficult.
Q No 3.How to made NFA corresponding to the closure of an FA ?
While generating NFA corresponding to closure of an FA one should take care of the null
string. Simple way to accept null string is declare initial state, final as well. But in this way a
lot of other strings will also be accepted. Therefore, accurate way is draw another state.
Declare the new state initial as well as final. Connect the new state with the states originally
connected with the old start state with the same transitions as the old start state. Newly drawn
diagram will be an NFA representing the language closure of the given FA
Q No 4.What is the difference between Union of two FA’s , Concatenation of two FA’s
and closure of two FA’s ?
Consider two FA's given below
a
a
b
b
a
b
a
b
Y2+
Y1X2+
X1FA1
FA2
Here FA1 accepts all strings ending in a and FA2 accepts all strings ending b.
An FA corresponding to FA1UFA2 will accept all the strings ending in a or ending in b. for
example, aba,bbaaab,bbb
An FA corresponding to FA1FA2 will accept all the strings whose first substring belongs to
FA1 and second substring belongs to FA2. for example, ababab, bbabbb.
An FA corresponding to FA1* will accepts all the strings of FA1 including null string. if FA1
represents RE r1 then FA1* will correspond to RE r1*.
Question: FAQ's about Lectures 21 to 25
Automata Theory FAQ's about
Lectures
21 to 25
Answer:
Q No 1.How Moore and Mealy machine works in Computer Memory what is their
importance in Computing ?
Q No 2.What is sequential circuit ?
Q No 1.How Moore and Mealy machine works in Computer Memory what is their
importance in Computing ?
Mealy & Moore Machines work in computing as incrementing machine & 1's complement
machine etc. These operations as basic computer operations so these machines are very
important.
Q No 2.What is sequential circuit ?
Sequential Circuit:
1. A sequential circuit contains a memory component.
2. The memory component provides a state input. A flip-flop is often used as a memory
component.
3. The state variable indicates the states of the sequential machine, i.e. the status or stage
or progress of the whole event.
4. The state of a sequential circuit is indicated by the output of a flip-flop. A single flipflop
can be used to indicate two states (q=0 and q=1). When there are more than two
states, additional flip-flops are used. Given n flip-flops, a total of 2n states can be
represented.
5. In other words, a sequential machine can be put into a number of different states
depending on the particular inputs given.
6. The output is a function of both the Present Inputs and the Present States.
7. In addition to the outputs, the circuit must also generate an update to the memory
components so that the state of the machine can also be changed with respect to the
new inputs. The update is called the Next State Function and is also a function of the
Present Inputs and the Present States.
8. Both the output functions and the Next State Functions are combinational circuits.
Z=f(X,St)
S=g(X,St)
9. The superscript t indicates the present time period while the superscript (t+1) indicates
the next time period.
10. The characteristic of a sequential circuit is completely defined by a state transition
diagram that enumerates all possible transitions for every possible input combination.
FAQ's about Lectures 26 to 30
Answer:
Automata Theory
FAQ's about Lectures 26 to 30
Q No 1.What is the concept of Pumping Lemma I and II and what is the difference
between
pumping Lemma 1 and pumping Lemma 2 ?
Q No 2. What is the significance of Pumping Lemma II ?
Q No 3.Moore and Mealy machine?
Q No 1.What is the concept of Pumping Lemma I and II and what is the difference
between
pumping Lemma 1 and pumping Lemma 2 ?
In fact PLI & PLII are same (A way to recognize Non Regular language). The only
difference is that
the
conditions in pumping lemma II are more stricter than Pumping Lemma I some language that
are
difficult
to proof Non Regular by Pumping Lemma I are proved Non Regular by pumping Lemma II
easily.
Further mare in pumping lemma I we have to generate all words to of a language but in
Pumping
Lemma II
we have to generate a single word to prove a language non regular.
Explanation:
Some languages like PALINDROME that are proved to be regular by first version
due to some of their symmetrical words when we pump these words they remain to be
the parts of the language like
bbabb
By pumping lemma 1
Let y = a
Now repeating y three times results in
bbaaabb
That is also a valid word of PALINDROME so by pumping lemma I PALINDROME can not
be
proved
non regular, so there was the need of pumping lemma version version 2.
Now consider for the word
bbabb
if we take N=2
Then by pumping y (let we take it b ) two times results in
bbbbabb
That word is not in PALINDROME.
But if we take N=3 and y = a
Then by pumping y two times results in
bbaaabb
That word is in PALINDROME. So be careful in taking total no of states of the FA
and also the repeating factor (y) to prove an infinite language non regular you
need to prove only one word that is not part of the language.
Q No 2. What is the significance of Pumping Lemma II ?
The significance of 2nd version of 'pumping lemma' is that there are some infinite non
regular
languages
like PALINDROME we can built FA that can accept there certain words but if we increase
the
length of
their words that FA don't accept these words so by pumping lemma version I it is very
difficult to
prove
them non regular but with the second version we can prove that a language is Non regular
even it's
some
words may be accepted by some FA's.
See page 195 of the book for further example.
Q No 3.Moore and Mealy machine?
1. In order to run a string on a Mealy or Moore machine, you can take directions from
transition
table.
Running string on Mealy or Moore machine is similar to running string on a FA. For
example, if
want to
run abba on the machine, take start from initial state. Check what is the transition for a, what
state it
goes.
After that check what is the path of b from that state and so on. In this way you will be able
to run
whole of
the string. Note that there is no final state in Mealy or Moore machine. So there is no case of
acceptance or
rejection of string. You just have to determine what the output is. I hope that will clear your
mind for
further clarification please listens to your lecture carefully.
2. The string is taken for the testing purposes. You can take any sort of string and determine
its
output using
machine.
Question: FAQ's about Lectures 31 to 35
Answer:
Automata
Theory
FAQ's about Lectures 31 to
35
Q No 1.What is the difference between semiword and word please also give me any
example regarding this?
Q No 2.What does mean the LANGUAGE IS CLOSED?
Q No 3.What are the Productions?
Q No 4.What is the difference between concatenation and intersection of two FA's
also what is the difference among Union of two FA's and addition of them?
Q No 1.What is the difference between semiword and word please also give an
example regarding this?
Word:
A word is complete combinations of terminals only e.g. abba or ab or a or null string.
Semiword:
A semiword is a string of terminals (may be none) concatenated with exactly one nonterminal
on the right i.e. a semi word, in general, is of the following form
(terminal)(terminal) ------------- (terminal)(nonterminal)
For example
aaaaaaB , aabbaaaA , A.
What is the difference between derivation tree and total tree ?
A Derivation tree is the one that shows how to derive any specific word of the language
described by CFG but Total Language Tree shows all words of the Language described by
CFG on it
Q No 2.What does mean the LANGUAGE IS CLOSED?
When we say that a Language is closed it is always with respect to certain operation.
A simple example may be that the set of integers is closed under addition. It means when we
take two numbers from set of integers say 3, 7 the result of their addition would also be in the
set of integers.
Similarly if the result of an operation on the words of a language results in the word of the
same language we say that the language is closed under that operation.
Q No 3.What are the Productions?
Productions are the grammatical rules and regulations. These rules express the behavior of
CFG. Using production in CFG terminals are converted into non-terminals and when all the
terminals are converted using productions, a word is acquired.
Q No 4.What is the difference between concatenation and intersection of two FA's
also what is the difference among Union of two FA's and addition of them?
In intersection of two FA's only those strings are accepted which are independently accepted
by both FA‟s, while in concatenation of two FA‟s only those strings will be accepted in
which first part of string is accepted by first FA and remaining part of string is accepted by
the second FA.
While taking union of two FA‟s one can represent it using + sign. So (FA1 U FA2) and (FA
+ FA2) both are same. There is no difference between them.
Question: FAQ's about Lectures 36 to 40
Answer:
Automata Theory
FAQ's about Lectures 36 to 40
Q No 1.What is the Difference between Nullable and Null
production? How to make eliminate Nullable and for Null
Productions from the CFG ?
Q No 2. Is it possible to make CFG for infix and postfix expression's
using derivation tree ?
Q No 3 what is the uses of push down automata in computing ?
Q No 4 What is difference between PUSH DOWN STACK and PUSH
DOWN STORE ?
Q No 5 How we can distinguish between "CFG" and "CNF" in the
questions ?
Q No 6.What is meant by the terms stack consistence and input
tape consistence ?
Q No 7 What is the concept of unit production ?
Q No 8 Why Context Free Grammars are called "Context Free?
Q No 9. What is Unit Production?
Q No 10.What is Left most Derivation in CFG?
Q No 1.What is the Difference between Nullable and Null production? How to make
eliminate Nullable and for Null Productions from the CFG ?
The production of the form
nonterminal ® L
is said to be null production.
Example:
Consider the following CFG
S ® aA|bB|L, A ® aa|L, B ® aS
Here S ® L and A ® L are null productions.
A production is called nullable production there is a derivation that starts at Non Terminal and
leads to L i.e.
S -----------> aA | bB | aa
A-------------> C | bb
C--------------> L
Here A nullable Non Terminal due to Nullable production A---------------> C as C leads to null.
Example:
Consider the following CFG
S ® XY, X ® Zb, Y ® bW
Z ® AB, W ® Z, A ® aA|bA|L
B ®Ba|Bb|L.
Here A ® L and B ® L are null productions, while Z ® AB, W ® Z are nullable productions.
Method:
Delete all the Null productions and add new productions e.g.
Consider the following productions of a certain CFG X ® aNbNa, N ® L, delete the production
N ® L and using the production
X ® aNbNa, add the following new productions
X ® aNba, X ® abNa and X ® aba
Thus the new CFG will contain the following productions X ® Nba|abNa|aba|aNbNa
Note: It is to be noted that X ® aNbNa will still be included in the new CFG.
Method:
Consider the following CFG
S ® XY, X ® Zb, Y ® bW
Z ® AB, W ® Z, A ® aA|bA|L
B ®Ba|Bb|L.
Here A ® L and B ® L are null productions, while Z ® AB, W ® Z are nullable productions.
The new CFG after, applying the method, will be
S ® XY
X ® Zb|b
Y ® bW|b
Z ® AB|A|B
W®Z
A ® aA|a|bA|b
B ®Ba|a|Bb|b
Note: While adding new productions all Nullable productions should be handled with care. All
Nullable productions will be used to add new productions, but only the Null production will be
deleted
Q No 2. Is it possible to make CFG for infix and postfix expression's using derivation
tree ?
Derivation tree is only used to derive words of language that is described by a CFG. Yes, we can create CFG for
languages infix expressions, postfix expressions.
Q No 3 what is the uses of push down automata in computing ?
PDA is just an enhancement in FAs. i.e Memory is attached with machine that recognizes some language. FA is
basic structure for most advanced electronic machines such as computer etc.
Q No 4 What is difference between PUSH DOWN STACK and PUSH DOWN STORE ?
No difference at all. Both terms are used to describe memory structure attached with FAs to store some
characters in it.
Q No 5 How we can distinguish between "CFG" and "CNF" in the questions ?
Chomsky Normal Form (CNF)
If a CFG has only productions of the form
nonterminal ---------� string of two nonterminals
or
Nonterminal -----------� one terminal
Then the CFG is said to be in Chomsky Normal Form (CNF).
Thus if the given CFG is in the form specified above it will be called in CNF.
Q No 6.What is meant by the terms stack consistence and input tape consistence ?
Term Stack consistent means we can pop any character from the top of the stack only. PDA should not be able
to pop any character other than that is present on the top of the stack.
Term Tape consistent means we can read only the first letter on the tape not any other letter of the tape after the
first one.
Q No 7 What is the concept of unit production ?
The productions of the form
one Nonterminal --------� one Nonterminal
Are called unit productions.
For example
S --------� A (Unit Produciton)
A--------� a | b
Here there is no need of Unit Production S→ A. we can directly write
S --------� a | b
Q No 8 Why Context Free Grammars are called "Context Free?
Context Free Grammars are called context free because the words of the languages of Context Free Grammars
have words like “aaabbb”(PALINDROME). In these words the value of letters (a , b) is the same on whatever
position they appear. On the other hand in context sensitive grammars their value depend on the position they
appear in the word a simple example may be as follows
Suppose we have a decimal number 141 in our language . When compiler reads it, it would be in the form of
string. The compiler would calculate its decimal equivalent so that we can perform mathematical functions on it.
In calculating its decimal value , weight of first “1” is different than the second “1” it means it is context
sensitive (depends on in which position the “1” has appeared).
i.e.
1*102 + 4*101 + 1* 100 = 14
(value of one is 100) (value of one is just one)
That is not the case with the words of Context Free Languages. (The value of “a” is always same in whatever
position “a” appears).
Q No 9. What is Unit Production?
The production in which one non-terminal leads to only one non-terminal.
Q No 10.What is Left most Derivation in CFG?
It is a method of generation of strings from a CFG starting from left most letter of the string.
Question: FAQ's about Lectures 41 to 45
FAQ's about Lectures 41 to 45
Q No 1.Give an example of converting a CFG to CNF?
Q No 2.In the lecture 41 's example, we have converted PDA to conversion form and a
word 'aaaabb' is derived from this conversion form PDA. What are the derivation
steps.
Q No 3.How to differentiate between "wanted" and "unwanted branch" ?
Q No 4.What is the difference between intersection and union of a language?
Q No 5.What is the difference between Context free languages and regular
languages?
Q No 6.What is the difference between Moore and Mealey machines?
Q No 7.What does the following terms mean ?
i. STACK Consistent
ii. Y-able Paths
iii. Working string
iv. Semi Word
Q No 1.Give a example of converting a CFG to CNF?
Consider the CFG given below
S→ ABC
A→ aa | b
B→ c
C→d
Its CNF will be
S→ DC
D → AB
A→ EE | b
E→a
B→c
C→d
Q No 2.In the lecture 41 's example, we have converted PDA to conversion form and a
word 'aaaabb' is derived from this conversion form PDA. What are the derivation
steps.
The PDA converted to conversion form has some specific features that are important to
understand first. These features are
The states named START, READ, HERE and ACCEPT are called joints of the machine.
With the help of the conversion form we have been able to achieve that POP state has only
one path out of it and the path taking (multiple paths) decisions take place only on the READ
state.
The word 'aaaabb' is generated as follows from the PDA
START-POP4-PUSH $
This step pops $ and then pushes it to ensure that stack contains $ at the beginning.
READ1-POP6-PUSH $-PUSH a
As first time after reading "a" there is $ at the top of stack so we will follow path segment
READ1-POP6-PUSH $-PUSH a
READ1-POP5-PUSH a-PUSH a
Now a is on the top of the stack so we will follow READ1-POP5-PUSH a-PUSH a
READ1-POP5-PUSH a-PUSH a
Again following same segment for a
READ1-POP5-PUSH a-PUSH a
Again following same segment for a
READ1-POP1- HERE-POP2
As we read b on input tape.
READ2-POP1-HERE-POP2
As we read b on input tape.
READ2-POP3-ACCEPT.
As we read Δ from the input tape
Q No 3.How to differentiate between "wanted" and "unwanted branch" ?
When we derive a word in Top down parsing beginning with the starting Non Terminal the
branches of the tree that do not lead to our required word are left aside these branches are
called unwanted branches.
For example for CFG
S----->AA
A----->a | b
If we want to generate the word "aa" we will leave the branch generated by the production A----->b.
Q No 4.What is the difference between intersection and union of a language?
Intersection of two languages will consist of all those words which are in both languages
while union of two languages will consist of all those words which are present in at least one
language.
Symbol for intersection is ∩ and for union is U.
Q No 5.What is the difference between Context free languages and regular
languages?
Regular languages can be represented by FA‟s because we do not need any memory to
recognize (accept or reject them on FA) them but there is another class of languages that can
not be represented by FA‟s because these languages require that we have some memory (with
the help of memory we can store letters of the string we are checking so that we can compare
them with next coming letters in the string).
For example language anbn requires that we must store a‟s and then compare their count with
next coming b‟s so that we can check whether a‟s are equal to b‟s or not.
Due to this reason we use Context Free Grammars to represent them because we can5t write
RE‟s for them.
So Context Free Languages represent a broader category this category also include regular
languages as subcategory. It means that context free languages include regular languages as
well as some other languages.
Q No 6.What is the difference between Moore and Mealey machines?
In Mealy Machine we read input string letters and generate output while moving along
the paths from one state to another while in Moore machine we generate output on
reaching the state so the output pattern of Moore machine contains one extra letter
because we generated output for state q0 where we read nothing.
Q No 7.What does the following terms mean
i. STACK Consistent
ii. Y-able Paths
iii. Working string
iv. Semi Word means
Stack consistence means that in the PDA converted in the conversion form, when we
follow a path segment (which is formed by combining start, read or here state with
next read, here or accept state on the path) along the PDA its pop state should have
the path for the same letter that is present on the top of the stack at that stage. If this
doesn‟t happen our PDA will crash because in conversion form of the PDA the pop
state has only one letter path, so if we could not be able to find that letter on the top of
the stack our PDA will crash (if will not find path where to go from that state)
Working string means the string present on the input tape.
Y-able Paths means that when we follow a certain sequence of rows from the row
table to generate a path for a word form start state to accept state. The path (sequence
of rows) should be stack as well as joint consistent it means that rows should end at
the same read or here state (join consistency ) and the rows should be able to pop the
letter from the top that is indicated in the pop state of the row.
Semi word is the string of terminals it may be null string ending with a Non terminals
on the right.
For example some semi words are
aaS
aabbA
B
Question: Is Automata Theory is a Programming Subject or theoretical?
Answer:
Automata theory is the study of abstract computing devices, or "machines". This
topic goes back to the days before digital computers and describes what is
possible to compute using an abstract machine.
These ideas directly apply to creating compilers, programming languages, and
designing applications. They also provide a formal framework to analyze new
types of computing devices, e.g. biocomputers or quantum computers
Question: What are practical Examples of the implications of Automata Theory
and the formal Languages?
Answer:
Grammars and languages are closely related to automata theory and
are the basis of many important software components like:
– Compilers and interpreters
– Text editors and processors
– Text searching
– System verification
Question: What are the Types of Automata?
Answer: The Types of Automata Theory are
1. Finite Automata
2. Regular Languages
3. Linear-bounded Automata
4. Context Sensitive Languages
5. Push-Down Automata
6. Context Free Languages
7. Turing Machines
8. Recursively innumerable languages
There are others as well like,
Random Access Machines
Parallel Random Access Machines
Arrays of Automata
Question: How types of Automata Differ?
Answer: They differ in the following areas
1. Complexity (or Simplicity)
2. Power
3. In the function that can be computed.
4. In the languages that can be accepted.
Question: What is the difference between the alphabet and an element of a set?
Answer:
Alphabets is a set of letters nothing else but a set of strings (elements) can have
more than one letters in one string.
Question: Difference between Palindrome and Reverse function?
Answer: The language consisting of Λ and the strings s defined over Σ such that
Rev(s)=s.
It is to be denoted that the words of PALINDROME are called palindromes.
Reverse (w) = w
Example: Σ={a,b},
PALINDROME={Λ , a, b, aa, bb, aaa, aba, bab, bbb, ...}
If a is a word in some language L, then reverse (a) is the same string of letters spelled
backwards,
called the reverse of a.
e.g
reverse (xxx) = xxx
reverse (623) = 326
reverse (140) = 041
Question: Define Strings?
Answer: Concatenation of finite letters from the alphabet is called a string.
e.g If Σ= {a,b} then a language L can be defined as
L = {a, abab, aaabb, ababababababababab,...............}
it's mean all words with a's more or equal to b's
Question: Define empty or null strings?
Answer: Concatenation of finite letters from the alphabet is called a string.
Sometimes a string with no symbol at all is used, denoted by (Small Greek letter Lambda) λ
or (Capital Greek letter Lambda) Λ, is called an empty string or null string.
Question: Difference between string and word?
Answer: Any combination of letters of alphabet that follows rules of language is called a
word.
A string is a finite sequence of symbols from an alphabet.
Question: There are as many palindromes of length 2n as there are of length 2n-1, please
explain?
Answer: If we try to create palindromes then middle elements (2 in even palindromes & 1 in
odd
palindrome) does not cause any change in no. of palindromes
Defining the language PALINDROME, of length 2n and 2n-1 defined over S = {a,b}
e.g if we take n= 2 for 2n
Length (2n) = 4 and string can be written as
{aaaa, abba, baab, bbbb}
And if we take n = 2 for 2n-1
Length (2n-1) = 3 and string can be written as
{aaa, aba, bab, bbb}
Question: Define Kleene Star?
Answer: Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the
collection of
all strings defined over Σ, including Λ.
It is to be noted that Kleene Star Closure can be defined over any set of strings.
Examples
If Σ = {x}
Then Σ* = {Λ, x, xx, xxx, xxxx, ….}
If Σ = {0,1}
Then Σ* = {Λ, 0, 1, 00, 01, 10, 11, ….}
If Σ = {aaB, c}
Then Σ* = {Λ, aaB, c, aaBaaB, aaBc, caaB, cc, ….}
Note:
Languages generated by Kleene Star Closure of set of strings, are infinite languages. (By
infinite language, it is supposed that the language contains infinite many words, each of finite
length).
Question: Why do not we can write" ba" in the set of PALINDROME while it is reverse of
"ab".
Answer: The language consisting of Λ and the strings s defined over Σ such that Rev(s)=s.
It is to be denoted that the words of PALINDROME are called palindromes.
Example
For Σ={a,b},
PALINDROME={Λ , a, b, aa, bb, aaa, aba, bab, bbb, ...}
All two length string cannot satisfied the palindrome. aa and bb in palindrome but
ba and ab are not in palindrome.
Question: What are the steps of Recursive Definition of Languages?
Answer: A recursive definition is characteristically a three-step process.
First, we specify some basic objects in the set.
Second, we give rules for constructing more objects in the set from ones we already know.
Third, we declare that no objects except those constructed in this way are allowed in the set.
Question: Strings that ending in "a " and strings containing exactly one "a".
Answer: Its means all string ending in a
e.g Σ= {a, b}
{a, aa, ba, aba, baa,…….}
Exactly a, defined over Σ= {a, b}
{ab, ba, abb, bba,……... }
Question: What is Lexical Analyzer?
Answer: The first phase of the compiler is the lexical analyzer, also known as the scanner,
which
recognizes the basic language units, called tokens.
• The exact characters in a token is called its lexeme.
• Tokens are classified by token types, e.g. identifiers, constant literals, strings,
operators, punctuation marks, and key words.
• Different types of tokens may have their own semantic attributes (or values) which
must be extracted and stored in the symbol table.
• The lexical analyzer may perform semantic actions to extract such values and insert
them in the symbol table.
Question: What is accepting string language?
Answer: The strings which follow rules for the language are accepted in language.
• Let u and v be strings. Then uv denotes the string obtained by concatenating u with
v, that is, uv is the string obtained by appending the sequence of symbols of v to that
of u. For example if u = aab and v = bbab,
then uv = aabbbab. Note that vu = bbabaab uv. We are going to use first few
symbols of English alphabet such as a and b to denote symbols of an alphabet and
those toward the end such as u and v for strings.
Question: What is transition table?
Answer: A complete transition table contains one column for each character. To save space,
table compression may be used. Only non-error entries are explicitly represented in
the table, using hashing, indirection or linked structures.
Tabular representation of a function that takes two arguments and returns a value
01
� q0 q2 q0
*q1 q1 q1
q2 q2 q1
• Rows correspond to states
• Columns correspond to inputs
• Entries correspond to next states
• The start state is marked with an arrow
• The accepting states are marked with a star
Question: What does it means by the transition?
Answer: Transition means which letter, after being read, is transfer from which place to
which place.
It
is necessary to show transition of every letter from each and every state.
Question: What is Null?
Answer: Λ is a string having no letter in it. e.g ( A box having no object in it).
Let us observe that if the alphabet has no letters, then its closure is the language with the null
string as its only word, because Λ is always a word in a Kleen closure. Symbolically,
we write
if Σ = {the empty set}
then Σ* = {Λ},
This is not the same as
if S = {Λ}
then S* = {Λ}
which is also true but for a different reason, that is ΛΛ = Λ.
Example
If L is any language, then
LΛ = ΛL = L
If Λ string concatenates with any string S, it does not cause any change in the string S, if we
use Λ in any string then it generates some result that is below here
Λ for both side then string is ΛaaΛ = aa
b for left and Λ for right then string is baaΛ = baa
Λ for left and b for right then string is Λaab = abb
Question: What is the difference between Regular Languages and Non Regular Languages?
Answer: The language determined by a regular expression is regular otherwise non regular.
Question: What is NFA?
Answer: Nondeterminism plays a key role in the theory of computing. A nondeterministic
finite state
automaton is one in which the current state of the machine and the current input do not
uniquely determine the next state. This just means that a number of subsequent states (zero
or more) are possible next states of the automaton at every step of a computation.
Of course, nondeterminism is not realistic, because in real life, computers must be
deterministic. Still, we can simulate nondeterminism with deterministic programs.
Furthermore, as a mathematical tool for understanding computability, nondeterminism is
invaluable.
As with deterministic finite state automata, a nondeterministic finite state automaton has five
components.
• a set of states
• a finite input alphabet from which input strings can be constructed
• a transition function that describes how the automaton changes states as it processes
an input string
• a single designated starting state
• a set of accepting states
The only difference lies in the transition function, which can now target subsets of the states
of the automaton rather than a single next state for each state, input pair.
Question: What is a main difference between NFA and FA?
Answer: Finite Automata (FA)
• A finite automaton with unique transitions from each state.
• There are no choices
• There is only 1 letter of the alphabet per transition (the label on the edges
in the graph is limited to 1)
• Λ transitions are not allowed.
•
No implied trap states. That is, if the letter of alphabet has n letters in it,
every state will have n edges coming out of it. If the letters are not part of a
valid word, then the edges will go into a special state, called the trap
states. Trap states are the NO states.
Nondeterministic Finite Automaton (NFA)
• Has the freedom to do various different moves when in a state and seeing
some input
• This is modeled mathematically as
The ability to be in various states at once
Accepting a string whenever at least one of those states is accepting.
Question: How to obtain 9's complement?
Answer: The (r – 1)‟s Complement
Given a positive number N is base r with an integer part of n digits and a fraction part of m
digits, the (r-1)‟s complements of N is defined as
rn –r-m – N. Some numerical examples follow:
The 9‟s complement of (52520)10 is (105 – 1 – 52520) = 99999 – 52520 = 47479.
No fraction part, so 10-m = 100 = 1.
The 9‟s complement of (0.3267)10 is (1 – 10-4 – 0.3267) = 0.9999 – 0.3267 = 0.6732
No integer part, so 10n = 100 = 1.
The 9‟s complement of (25.639)10 is (102 – 10-3 – 25.639) = 99.9999 - 25.63967 = 74.360
Question: What is DELAY box?
Answer: It is a component which held input for some time and then forwards it just a holder.
Question: What is the difference between pumping Lemma 1 and pumping Lemma 2?
Answer: Infact PLI & PLII are same (A way to recognize Non Regular language). The only
difference
is in PLII we take care about the substring x & y that length (x) + length (y) less than or equal
no. of state of machine. This is because through PLI palindrome (that is Non Regular) is
proved to be regular and through PLII this problem is fixed.
Question: What is pumping lemma? And what is history?
Answer: A theorem to check validity (Regularity) of an infinite language should not be used
with
finite languages. Whenever an infinite is regular then there must be a loop (circuit) because
without a loop means infinite no. of states that is not possible practically. (Machine can have
finite states only)
Question: What is the difference between semi word and word?
Answer: A word is complete combinations of terminals only e.g. abba or ab or a or null
string.
Semiword: A semiword is a string of terminals (may be none) concatenated with exactly one
nonterminal on the right i.e. a semiword, in general, is of the following form
(terminal)(terminal)… (terminal)(nonterminal)
Question: What is the difference between derivation tree and total tree?
Answer: A Derivation tree is the one that shows how to derive any specific word of the
language
described by CFG but Total Language Tree shows all words of the Language described by
CFG on it.
Question: How to identify a production by it, ambiguity will be removed?
Answer: It is a matter of practice that one can know how to remove ambiguity from it, only
practice
makes you efficient enough to do it in less time.
Question: Difference between Nullable and Null production? How to make CFG for Nullable
and for
Null?
Answer: The production of the form
nonterminal ® L
is said to be null production.
Example:
Consider the following CFG
S ® aA|bB|L, A ® aa|L, B ® aS
Here S ® L and A ® L are null productions.
A production is called nullable production if it is of the form
N®L
or
there is a derivation that starts at N and leads to L i.e.
N1 ® N2, N2 ® N3, N3 ® N4, …, Nn ® L, where N, N1, N2, …, Nn are
non terminals.
Example:
Consider the following CFG
S ® XY, X ® Zb, Y ® bW
Z ® AB, W ® Z, A ® aA|bA|L
B ®Ba|Bb|L.
Here A ® L and B ® L are null productions, while Z ® AB, W ® Z
are nullable productions.
Method:
Delete all the Null productions and add new productions e.g.
Consider the following productions of a certain CFG X ® aNbNa, N ®
L, delete the production
N ® L and using the production
X ® aNbNa, add the following new productions
X ® aNba, X ® abNa and X ® aba
Thus the new CFG will contain the following productions X ®
Nba|abNa|aba|aNbNa
Note: It is to be noted that X ® aNbNa will still be included in the new
CFG.
Method:
Consider the following CFG
S ® XY, X ® Zb, Y ® bW
Z ® AB, W ® Z, A ® aA|bA|L
B ®Ba|Bb|L.
Here A ® L and B ® L are null productions, while Z ® AB, W ® Z are
nullable productions. The new CFG after, applying the method, will be
S ® XY
X ® Zb|b
Y ® bW|b
Z ® AB|A|B
W®Z
A ® aA|a|bA|b
B ®Ba|a|Bb|b
Note: While adding new productions all Nullable productions should be
handled with care. All Nullable productions will be used to add new
productions, but only the Null production will be deleted.
Question: Is it possible to make CFG for infix and postfix expression‟s using derivation tree?
Answer: Derivation tree is only used to derive words of language that is described by a CFG.
Yes,
we
can create CFG for languages infix expressions, postfix expressions.
Question: What are the uses of push down automata in computing?
Answer: PDA is just an enhancement in FAs. i.e Memory is attached with machine that
recognizes some language. FA is basic structure for most advanced electronic
machines such as computer etc.
Question: What is difference between PUSH DOWN STACK and PUSH DOWN STORE?
Answer: No difference at all. Both terms are used to describe memory structure attached with
FAs to
store some characters in it.
Question: How to accommodate NULL string if it is part of language during converting from
CFG to
CNF and building FA's?
Answer: When we convert CFG to CNF and Null is a part of language then null string is not
part of
language in CNF. This is the only change a language gets in CNF. When we draw an FA for
a CFG, there is no change in language and simply draws FA that accepts the language of
CFG.
Question: How to accommodate NULL string if it is part of language during converting from
CFG to
CNF and in building PDA?
Answer: When we convert CFG to CNF and Null is a part of language then null string is not
part of
language in CNF. This is the only change a language gets in CNF. When we draw an PDA
for a CFG, there is no change in language and simply draws PDA that accepts the language
of
CFG.
Question: What is Push down Automata?
Answer: Pushdown Automaton (PDA), consists of the following
• An alphabet S of input letters.
• An input TAPE with infinite many locations in one direction. Initially the input string
is placed in it starting from first cell; the remaining part of the TAPE is empty.
• An alphabet G of STACK characters.
• A pushdown STACK which is initially empty, with infinite many locations in one
direction. Initially the STACK contains blanks.
• One START state with only one out-edge and no in-edge.
• Two halt states i.e. ACCEPT and REJECT states, with in-edges and no out-edges.
• A PUSH state that introduces characters onto the top of the STACK.
• A POP state that reads the top character of the STACK (may contain more than one
out-edges with same label).
•
A READ state that reads the next unused letter from the TAPE (may contain more
than one out-edges with same label).
Question: Why we study Automata?
Answer: Automata theory is the study of abstract computing devices, or "machines". This
topic goes back to the days before digital computers and describes what is possible
to compute using an abstract machine.
These ideas directly apply to creating compilers, programming languages, and
designing applications. They also provide a formal framework to analyze new
types of computing devices, e.g. biocomputers or quantum computers. Finally, the
course should help to turn you into mathematically mature computer scientists
capable of precise and formal reasoning.
More precisely, we'll focus primarily on the following topics. Don't worry about
what all the terms mean yet, we'll cover the definitions as we go:
1. Finite state automata: Deterministic and non-deterministic finite state machines;
regular expressions and languages. Techniques for identifying and describing
regular languages; techniques for showing that a language is not regular. Properties
of such languages.
2. Context-free languages: Context-free grammars, parse trees, derivations and
ambiguity. Relation to pushdown automata. Properties of such languages and
techniques for showing that a language is not context-free.
3. Turing Machines: Basic definitions and relation to the notion of an algorithm or
program. Power of Turing Machines.
4. Undecidability: Recursive and recursively enumerable languages. Universal
Turing Machines. Limitations on our ability to compute; undecidable problems.
5. Computational Complexity: Decidable problems for which no sufficient
algorithms are known. Polynomial time computability. The notion of NPcompleteness
and problem reductions. Examples of hard problems.
Question: What is valid and invalid alphabets explain with example?
Answer: Example 1
If s=abc is a string defined over Σ= {a,b,c}
then Rev(s) or sr = cba
Σ= {a,b}
s=abbaa
Rev(s)=aabba
When more then letter in the alphabet you have to be quite careful that don‟t reverse the
symbols however you write the letter from right to left.
Example 2
Σ= {B, aB, bab, d}
s=BaBbabBd
Rev(s)=dBbabaBB
Example 3
Σ= {ab, b, aa}
s=abbaa
Rev(s)=aabab
Σ1= {B, aB, bab, d} is valid alphabet as there is no letter in Σ1 that lies in start of any other
letter means all the tokens of any word (string) will be unique. Whereas in Σ2= {B, Ba, bab,
d} letter B lies in start of letter Ba.
This makes it difficult to decide which token to select at some point if B occurs in any string.
Question: Why we use Capital Letters for Languages. Is it possible to combine two languages
together
like EVEN-EVEN & EQUAL, and so on?
Answer: We use capital letter for our convenient and yes you can combine two languages.
Question: What are the rules to form WORDS in languages developed by Automata? Are
strings not
following any rule?
Answer: Rules are different for different languages.
e.g Σ={a,b}
The language L of strings of even length, defined over Σ= {a,b}, can be written as
Valid for even length L= {aa, bb, aabb, bbaa, baab, abba …..}
Invalid for even length L= {a, b, aaa, bbb, aba, bab, …….}
The language L of strings of odd length, defined over Σ= {a,b}, can be written as
Valid for odd length L1= {a, b, aaa, bbb, aba, bab, …….}
Invalid for odd length L= {aa, bb, aabb, bbaa, baab, abba …..}
Strings cannot follow any rule.
Question: What are graphs of palindromes of length 2n and length 2n-1?
Answer: Palindromes of even length are always symmetric about the middle line and
palindromes of
odd length are always symmetric about middle letter.
If we try to create palindromes then middle elements (2 in even palindromes & 1 in odd
palindrome) does not cause any change in no. of palindromes
Defining the language PALINDROME, of length 2n and 2n-1 defined over S = {a,b}
e.g if we take n= 2 for 2n
Length (2n) = 4 and string can be written as
{aaaa, abba, baab, bbbb}
And if we take n = 2 for 2n-1
Length (2n-1) = 3 and string can be written as
{aaa, aba, bab, bbb}
Question: How can we write a RE for a given number of words?
Answer: In example let us consider a finite language L that contains all the strings of a‟s
and b‟s of length three exactly:
L = {aaa aab aba abb baa bab bba bbb}
The first letter of each word in L is either an a or a b. The second letter of each
word in L is either an a or a b. The third letter of each word in L is either an a or a
b. So, we may write
L = language ((a+b)(a+b)(a+b))
Or
L = language ((a+b)3)
If we want to define the set of all seven-letter strings of a‟s and b‟s, we could write
(a+b)7 . In general, if we want to refer to the set of all possible strings of a‟s and
b‟s of any length whatsoever, we could write
(a+b)*
This is the set of all possible strings of letters from the alphabet Σ = {a, b}
including the null string. This is a very important expression and we shall use it
often.
Again, this expression represents a language. If we choose that * stands for 5, then
(a+b)*
gives
(a+b)5 = (a+b)(a+b)(a+b)(a+b)(a+b)
We now have to make five more choices: either a or b for the first letter, either a or
b for second letter, and so on.
21. Please explain that in some expression having more then one plus sign the
resulting string is only one from them or it can be more then one? For example if
there is an expression: a +b + c, with out any small bracket between them the
resultant string is "a or b or c" OR it cans both "a or b and c”,"a and b or c"
The resulting string is only one from them. Whenever we put + signs between n
words that means one option (only) out of all available.
Question: One Language generates many REs?
Answer: Sometimes we generate many Regular Expressions (RE) for one language these REs
are
called Equal RE.
Example:
Consider the following regular expressions
r1= (a + b)* (aa + bb)
r2= (a + b)*aa + ( a + b)*bb then
both regular expressions define the language of strings ending in aa or bb.
This RE (aa+bb) is separated by +. Whenever RE is separated by +, two possibilities occur
1. Before + part
2. After + part
(a+b)*aa comes before + part, means RE generate all strings that end with aa. (a+b)*bb
comes after + part this means RE generate all strings that end with bb. In short we can say r2
generates the language of strings ending either aa or bb this is equal to r1.
Question: Rules for determining RE for a given language defined on a set?
Answer: The following rules define the language associated with any regular expression:
Rule 1: The language associated with the regular expression that is just a single letter is that
one-letter word alone and the language associated with null is just {null}, a one-word
language.
Rule 2: If r1 is a regular expression associated with the language L1 and r2 is regular
expression associated with the language L2, then:
• The regular expression (r1)(r2) is associated with the product L1L2 that is the
language L1 times L2
language (r1r2) = L1L2
• The regular expression r1 + r2 is associated with the language formed by the union of
the sets L1 and L2:
language (r1 + r2) = L1 + L2
• The language associated with the regular expression (r1)* is L1*, the Kleene closure
of the set L1 as a set of words:
language(r1*) = L1*
Once again, this collection of rules proves recursively that there is some language associated
with every regular expression. As we build up a regular expression from the rules, we
simultaneously are building up the corresponding language.
Question: What is EVEN - EVEN LANGUAGE?
Answer: Even-Even means count of a's is even and cout of b's is also even.
Even + Even = Even (Proved)
So we can divide any string excluding Λ which is also in Even-Even in substrings of length 2
each. It gives us following combinations
aa, bb makes no change in string status
ab, ba create disorder in string status
so (aa+bb+(ab+ba)(aa+bb)*(ab+ba))*.
Question: What is tokenizing string?
Answer: Tokenize a string means make its valid units.
Question: What is whole star?
Answer: Whole star of any RE means all possible combinations of that RE including Λ.
Question: How to use + operator in Automata?
Answer: Plus Operation is same as Kleene Star Closure except that it does not generate Λ
(null
string),
automatically.
Question: How to know what is RE?
Answer: It is a matter of practice that you come to know what does an RE represent. You
may start
with simpler REs and later you will be able to recognize different REs gradually.
Question: Why we use null string in FA?
Answer: If null string is part of our language then we have to handle it in FA, its not
compulsion.
Question: What is tree structure?
Answer: A tree is a connected undirected graph with no simple circuits. Since a tree cannot
have a
simple circuit, a tree cannot contain multiple edges or loops. Therefore any tree must be a
simple graph.
Question: What is difference between (a, b) & (a + b)?
Answer: (a, b) & (a + b) are same and both represents either a or b.
Question: Difference between FA & TG?
Answer: Finite Automata (FA)
· A finite automaton with unique transitions from each state.
· There are no choices
· There is only 1 letter of the alphabet per transition (the label on the edges in the graph is
limited to 1)
· Λ transitions are not allowed.
· No implied trap states. That is, if the letter of alphabet has n letters in it, every state will
have n edges
coming out of it. If the letters are not part of a valid word, then the edges will go into a
special state,
called the trap states. Trap states are the NO states.
Transition Graphs (TG)
·TG are generalizations of FA.
· Can change state without an input.
· Can read more than one letter at a time.
· Can have a regular expression as a edge label.
· Can have more then one start state.
We are not bound in TG. We are only given a freedom or relation which we are not forced to
use. We may or may not use it on will.
In fact we enjoy freedom of staying at multiple places at one time in TGs while reading any
letter strings which provides us a facility that any one available path it leads us to final state,
word is accepted.
Question: Difference between (a+b)+ and (a+b)*?
Answer: (a + b)+ means, we repeat RE a + b infinite (any) no. of times but minimum once,
whereas
(a
+ b)* means we may repeat a + b any no. of times even zero times. () are only used to clear
(distinguish) the one RE from some other RE.
Question: What is length of string?
Answer: The length of a string indicates how many symbols are in that string.
For example, the string 0101 using the binary alphabet has a length of 4. The standard
notation for a string w is to use |w|.
For example:
Length of string: |0101| is 4.
Length of string: |0010| = 4, |aa| = 2, | |= 0
Question: After looking the on diagram how can we say it is TG or is FA?
Answer: Every FA is also a TG but not every TG is FA.
In every FA, every state shows transition of all letters of given alphabet but in any TG it is
not must. In TG, we may or may not show all letters transition according to requirement. We
can also show transitions on reading any strings in TGs but it is not possible in FAs.
Question: Differentiate between FA, TG and GTG?
Answer: Every FA is also a TG but not every TG is FA.
In every FA, every state shows transition of all letters of given alphabet but in any
TG it is not must. In TG, we may or may not show all letters transition according
to requirement. We can also show transitions on reading any strings in TGs but it
is not possible in FAs. In GTG Directed edges connecting some pair of states
labeled with regular expression.It may be noted that in GTG, the labels of
transition edges are corresponding regular expressions. In TG we write strings and
in GTG we are bound to write RE.
Question: Difference between even clumps and odd clumps?
Answer: Letters may be a's (for example) in even count at one place.
e.g.
aab = valid
baa = valid
aba = invalid
abab = invalid
Question: Difference between containing and consisting?
Answer: Containing something (e.g. R1) means R1 is there (must), whatever other things are,
we
don‟t
care.
Consisting something (e.g. R1) means only R1 is there all other things should be rejected.
Question: Define the main formula of Regular expressions? Define the back ground of
regular
expression?
Answer: Regular expressions are a notation that you can think of similar to a programming
language.
In fact, regular expressions are quite fundamental in some programming languages like perl
and applications like grep or lex. Regular expressions are similar to NFA and end up
describing the same things we can express with a finite automaton. However, regular
expressions are declarative in what strings are accepted, while automata are machines that
accept strings. We use Regular expressions for defining the languages.
Say that R is a regular expression if R is:
1. a for some a in the alphabet Σ, standing for the language {a}
2. Λ , standing for the language { Λ}
3. R1+R2 where R1 and R2 are regular expressions, and + signifies union
4. R1R2 where R1 and R2 are regular expressions and this signifies concatenation
5. R* where R is a regular expression and signifies closure
6. (R) where R is a regular expression, then a parenthesized R is also a regular expression
A set of strings from an alphabet. The set may be empty, finite or infinite.
The building blocks of regular languages are symbols, concatenation of symbols to make
strings (words), set union of strings and Kleene closure (denoted as *, also called the Kleene
star, it should be typed as a superscript but this is plain text.)
Informally, we use a syntax for regular expressions.
Using sigma as the set {0, 1} (an alphabet of two symbols)
01110 is a string starting with the symbol 0 and then concatenating 1, then 1, then 1, and
finally concatenating 0. No punctuation is used between symbols or strings that are
concatenated.
(01+10) is a union of the two strings 01 and 10. The set {01, 10}
(00+11)* is the Kleene closure of the union of 0 concatenated with 0 and 1 concatenated with
1.
The Kleene closure (star) is defined as the concatenation of none, one, two, or any countable
number strings it applies to.
Examples of Kleene star:
1* is the set of strings {Λ, 1, 11, 111, 1111, 11111, etc. }
This set is infinite.
(1100)* is the set of strings {Λ, 1100, 11001100, 110011001100, etc. }
(00+11)* is the set of strings {Λ, 00, 11, 0000, 0011, 1100, 1111, 000000, 000011, 001100,
etc. }
Note how the union ( + symbol) allows all possible choices of ordering when used with the
Kleene star.
(0+1)* is all possible strings of zeros and ones, often written as Σ * where Σ = {0, 1}(0+1)*
(00+11) is all strings of zeros and ones that end with either 00 or 11. Note that concatenation
does not have an operator symbol.
(w)+ is a shorthand for (w)(w)* w is any string or expression and the superscript plus, + ,
means one or more copies of w are in the set defined by this expression.
Question: Are S* and S+ same?
Answer: No because S+ means same as Kleene Star Closure except that it does not generate
Λ (null
string), automatically. So in the above example, there is no null string.
Concatenation of finite letters from the alphabet is called a string.
If we have S={a, bb, bab, abaab}, first we factorize the string like (a) (bb) (bab) (abaab) then
concatenate to each other and make more string to its concatenation but the string
abbabaabab is not in S* because the last member (ab) of the group does not belong to S, so
abbabaabab is not in S.
Question: What is set?
Answer: Set is a collection of distinct objects.
Question: How many Methods of defining the languages?
Answer: 1. You can describe a language in English like statement
2. You can define a language by putting all its words in a set
3. You can define a language in a mathematical way
4. You can define a language by Recursive Definition
5. You can define a language by Regular Expression
6. You can define a language by Finite Automata
7. You can define a language by Transition Graph
8. You can define a language by Grammar
Question: What is difference between Palindrome, Kleene star closure and plus operation?
Answer: The language consisting of Λ and the strings s defined over Σ such that Rev(s)=s.
or
A string x is a palindrome if xR=x.
It is to be denoted that the words of PALINDROME are called palindromes.
Reverse (w) = w
Example: Σ={a,b},
PALINDROME={Λ , a, b, aa, bb, aaa, aba, bab, bbb, ...}
If a is a word in some language L, then reverse (a) is the same string of letters spelled
backwards, called the reverse of a.
e.g
reverse (xxx) = xxx
reverse (623) = 326
reverse (140) = 041
Given Σ, then the Kleene Star Closure of the alphabet Σ, denoted by Σ*, is the collection of
all strings defined over Σ, including Λ.
Plus Operation is same as Kleene Star Closure except that it does not generate Λ (null string),
automatically.
Question: What is inside language?
Answer: Any language contains words in it and certain rules to validate strings for that
language.
Question: What is Equal RE?
Answer: Sometimes we generate many REs for one language these are called Equal RE.
Question: How can we make Finite Automaton from a language and a language from FA?
Answer: There is not any formal procedure to design FA for a language. This ability just
improves with time and practice.
Question: Could we just use +, - symbols with x not with y in FA?
Answer: Yes, you can use only + or – for the place of x and y, but remember when you don't
write +
or –, So you should write start and final at the beginning or ending state Or you should
indicated by an arrow and a final state by drawing box or another circle around its circle
because if you don't write how can we indicate the start and final state.
Question: Explain the language L of string, defined over Σ= {0,1}, having double 0's and
double 1's?
Answer: Language of strings with 00 or 11 means string that have substrings 00 or 11 in
them at
least.
Minimum words which are included in this language are 00 and 11. This language does not
accept null and it also does not accept 0 or 1.
Question: What are the difference between single 1 and 0 and double 1's and 0's?
Answer: 1. Consider the language L of strings, defined over
If Σ={0, 1}, having words with either 0‟s or 1‟s without null. The language L may be
expressed by RE
(0 + 1)+
When you make string by above RE you have all possible combination of 0‟s and 1‟s
except null
i.e {0, 1, 00, 01, 10, 11,……….}. Minimum words which are included in this language are
0 and 1.
2. Consider the language L of strings, defined over
If Σ={0, 1}, having double 0‟s or double 1‟s, The language L may be expressed by the RE
(0+1)* (00 + 11) (0+1)*
Double 1‟s and 0‟s means clumps of letter which will always come together. Minimum
words which are included
in this language are 00 and 11.
Question: On what basis we select initial and final states?
Answer: It depends on the expression given to us.
Question: How we know that the given expression has how many states?
Answer: There is not any formal procedure to know the number of states. This ability just
improves with time and practice.
Question: How will we develop the rules of transition?
Answer: Transition means which letter, after being read, is transfer from which place to
which place.
It
is necessary to show transition of every letter from each and every state.
Question: Can we accept the strings going from final to initial?
Answer: It is to be noted that if any state start from the final state it does not accept any
string. Even
it
does not accept the null string, because there is no path starting from initial state and ending
in final state.
Question: What are the basic rules to build FA?
Answer: One and only rule is to build a Finite Automata (FA) should accept all words of the
language
and reject all the words which are not part of the language. Any FA that ensures these above
things is the right FA for the language.
Note: One language can have many FA.
Question: What is Dead state?
Answer: The DEAD STATE is introduced to be able to make an automaton complete without
altering
its behavior.Bottom of Form
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CS402- MCQs:
For a given input, it provides the compliment of Boolean AND output.
NAND box (NOT AND)
DELAY box
OR box
AND box
It delays the transmission of signal along the wire by one step (clock pulse).
NAND box (NOT AND)
DELAY box
OR box
AND box
For the given input, it provides the Boolean OR output
NAND box (NOT AND)
DELAY box
OR box
AND box
For the given input, AND box provides the Boolean AND output.
True False
The current in the wire is indicated by 1 and 0 indicates the absence of the current.
True False
Any language that can not be expressed by a RE is said to be regular language.
True False
If L1 and L2 are regular languages is/are also regular language(s).
L1 + L2
L1L2
L1*
All of above
Let L be a language defined over an alphabet Σ, then the language of strings, defined over
Σ, not belonging to L, is called Complement of the language L, denoted by Lc or L’.
True False
To describe the complement of a language, it is very important to describe the ----------of that language over which the language is defined.
Alphabet
Regular Expression
String
Word
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For a certain language L, the complement of Lc is the given language L i.e. (Lc)c = Lc
True False
If L is a regular language then, --------- is also a regular language.
Lm
Ls
Lx
Lc
Converting each of the final states of F to non-final states and old non-final states of F to
final states, FA thus obtained will reject every string belonging to L and will accept every
string, defined over Σ, not belonging to L. is called
Transition Graph of L
Regular expression of L
Complement of L
Finite Automata of L
If L1 and L2 are two regular languages, then L1 U L2 is not a regular.
True False
De-Morgan's law for sets is expressed by,
CORRECT
If L1 and L2 are regular languages, then these can be expressed by the corresponding
FAs.
True False
L= language of words containing even number of a’s. Regular Expression is
(a+b)*aa(a+b)*
(b+ab*a)*
a+bb*aab*a
(a+b)*ab(a+b)*
The regular expression defining the language L1 U L2 can be obtained, converting and
reducing the previous ------------- into a ------------ as after eliminating states.
GTG, TG
FA, GTG
FA, TG
TG, RE
The language that can be expressed by any regular expression is called a Non regular
language.
True False
The languages -------------- are the examples of non regular languages.
PALINDROME and PRIME
PALINDROME and EVEN-EVEN
EVEN-EVEN and PRIME
FACTORIAL and SQURE
Let L be any infinite regular language, defined over an alphabet Σ then there exist three
strings x, y and z belonging to Σ* such that all the strings of the form for n=1,2,3, … are
the words in L. called.
Complement of L
Pumping Lemma
Kleene’s theorem
None in given
(21)
Languages are proved to be regular or non regular using pumping lemma.
True False
(22) ------------------- is obviously infinite language.
EQUAL-EQUAL
EVEN-EVEN
PALINDROME
FACTORIAL
(23) If, two strings x and y, defined over Σ, are run over an FA accepting the language
L, then x and y are said to belong to the same class if they end in the same state, no
matter that state is final or not.
True False
Myhill Nerode theorem is consisting of the followings,
L partitions Σ* into distinct classes.
If L is regular then, L generates finite number of classes.
If L generates finite number of classes then L is regular.
All of above
The language Q is said to be quotient of two regular languages P and R, denoted by--- if
PQ=R.
R=Q/P
Q=R/P Q=P/R
P=R/Q
If two languages R and Q are given, then the prefixes of Q in R denoted by Pref(Q in R).
True False
(27) Let Q = {aa, abaaabb, bbaaaaa, bbbbbbbbbb} and R = {b, bbbb, bbbaaa,
bbbaaaaa}
Pref (Q in R) is equal to,
{b,bbba,bbbaaa}
{b,bba,bbaaa}
{ab,bba,bbbaa}
{b,bba,bbba}
If R is regular language and Q is any language (regular/ non regular), then Pref (Q in R)
is ---------.
Non-regular
Equal
Regular
Infinite
"CFG" stands for _________
Context Free Graph
Context Free Grammar
Context Finite Graph
Context Finite Grammar
(29) ___________ states are called the halt states.
ACCEPT and REJECT
ACCEPT and READ
ACCEPT AND START
ACCEPT AND WRITE
(30) The part of an FA, where the input string is placed before it is run, is called
_______
State
Transition
Input Tape
Output Tape
In new format of an FA (discussed in lecture 37), This state is like dead-end non final
state
ACCEPT
REJECT
STATR
READ
For language L defined over {a, b}, then L partitions {a, b}* into …… classes
Infinite
Finite
Distinct
Non-distinct
The major problem in the earliest computers was
To store the contents in the registers
To display mathematical formulae
To load the contents from the registers
To calculate the mathematical formula
Between the two consecutive joints on a path
One character can be pushed and one character can be popped
Any no. of characters can be pushed and one character can be popped
One character can be pushed and any no. of characters can be popped
Any no. of characters can be pushed and any no. of characters can be popped
(35)
In pumping lemma theorem (x y^n z) the range of n is
n=1, 2, 3, 4……….
n=0, 1, 2, 3, 4……….
n=…….-3,-2,-1, 0, 1, 2, 3, 4……
n=…….-3,-2,-1, 1, 2, 3, 4……
(36) The PDA is called non-deterministic PDA when there are more than one out going
edges from……… state
START or READ
POP or REJECT
READ or POP
PUSH or POP
Identify the TRUE statement:
A PDA is non-deterministic, if there are more than one READ states in PDA
A PDA is never non-deterministic
Like TG, A PDA can also be non-deterministic
A PDA is non-deterministic, if there are more than one REJECT states in PDA
There is a problem in deciding whether a state of FA should be marked or not when the
language Q is infinite.
True False
If an effectively solvable problem has answered in yes or no, then this solution is called -------Decision procedure
Decision method
Decision problem
Decision making
The following problem(s) ------------- is/are called decidable problem(s).
The two regular expressions define the same language
The two FAs are equivalent
Both a and b
None of given
To examine whether a certain FA accepts any words, it is required to seek the paths from
------- state.
Final to initial
Final to final
Initial to final
Initial to initial
The high level language is converted into assembly language codes by a program called
compiler.
TRUE FALSE
Grammatical rules which involve the meaning of words are called --------------Semantics
Syntactic
Both a and b
None of given
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Grammatical rules which do not involve the meaning of words are called --------------Semantics
Syntactic
Both a and b
None of given
The symbols that can’t be replaced by anything are called ----------------Productions
Terminals
Non-terminals
All of above
The symbols that must be replaced by other things are called __________
Productions
Terminals
Non-terminals
None of given
(47) The grammatical rules are often called_____________
Productions
Terminals
Non-terminals
None of given
The terminals are designated by ________ letters, while the non-terminals are designated
by ________ letters.
Capital, bold
Small, capital
Capital, small
Small, bold
The language generated by __________ is called Context Free Language (CFL).
FA
TG
CFG TGT
(49) Σ = {a,b} Productions S→XaaX
X→aX
X→bX
X→Λ
This grammar defines the language expressed by___________
(a+b)*aa(a+b)*
(a+b)*a(a+b)*a
(a+b)*aa(a+b)*aa
(a+b)*aba+b)*
(50) S → aXb|b XaX → aX|bX|Λ The given CFG generates the language in English
__________
Beginning and ending in different letters
Beginning and ending in same letter
Having even-even language
None of given
(51) The CFG is not said to be ambiguous if there exists atleast one word of its
language that can be generated by the different production trees,
TRUE
FALSE
The language generated by that CFG is regular if _________
No terminal → semi word
No terminal → word
Both a and b
None of given
The production of the form no terminal → Λ is said to be null production.
TRUE FALSE
(54) A production is called null able production if it is of the form N → Λ
TRUE FALSE
(55) The productions of the form nonterminal → one nonterminal, is called _________
Null production
Unit production
Null able production
None of given
(56) CNF is stands for
Context Normal Form
Complete Normal Form
Chomsky Normal Form
Compared Null Form
Proof(Kleene’s Theorem Part II)
If a TG has more than one start states, then
Introduce the new start state
Eliminate the old start state
Replace the old start state with final state
Replace the old final state with new start state
Question # 2
While finding RE corresponding to TG, we connect the new start state to the old start
state by the transition labeled by
Select correct option:
a
b
null string
None of the given options
Question # 3 of 10 ( Start time: 05:49:03 PM ) Total Marks: 1
Which of the following regular expression represents same language? a. (a+ab)* b.
(ba+a)* c. a*(aa*b)* d. (a*b*)*
a+b)*a(a+b)*b(a+b)*+ (a+b)*b(a+b)*a(a+b)*.
{ x}*, { x}+, {a+b}*
Select correct option:
a and b
a and c
c and d
Question # 4 of 10 ( Start time: 05:50:32 PM ) Total Marks: 1
(a* + b*)* = (a + b)* this expression is __________
Select correct option:
True
False
Question # 5 of 10 ( Start time: 05:51:30 PM ) Total Marks: 1
Let FA3 be an FA corresponding to FA1+FA2, then the initial state of FA3 must
correspond to the initial state of
Select correct option:
FA1 only
FA2 only
FA1 or FA2
FA1 and FA2
Question # 6 of 10 ( Start time: 05:53:01 PM ) Total Marks: 1
Which of the following statement is NOT true about TG?
Select correct option:
There exists exactly one path for certain string
There may exist more than one paths for certain string
There may exist no path for certain string
There may be no final state
Question # 7 of 10 ( Start time: 05:54:06 PM ) Total Marks: 1
Kleene’s theorem states
Select correct option:
All representations of a regular language are equivalent.
All representations of a context free language are equivalent.
All representations of a recursive language are equivalent
Finite Automata are less powerful than Pushdown Automata.
Question # 8 of 10 (Start time: 05:55:36 PM) Total Marks: 1
What do automata mean?
Select correct option:
Something done manually
Something done automatically
Question # 9 of 10 ( Start time: 05:56:51 PM ) Total Marks: 1
A language accepted by an FA is also accepted by
Select correct option:
TG only
GTG only
RE only
All of the given
Question # 10 of 10 ( Start time: 05:58:16 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Select correct option:
(r1)(r2)
(r1 + r2)
(r2)(r1)
(r1)*
Question # 1 of 10 ( Start time: 11:12:33 PM ) Total Marks: 1
Alphabet S = {a, bc, cc} has __3__ number of letters
Select correct option:
radioBtn0
One
radioBtn1
Tw o
radioBtn2
Thre
radioBtn3
Four
333acscqq
Question # 2 of 10 ( Start time: 11:14:03 PM ) Total Marks: 1
If S = { x }, then S* will be
{x,xx,xxx,xxxx,…}
{^ ,x,xx,xxx,xxxx,…}
Question # 3 of 10 ( Start time: 11:15:11 PM ) Total Marks: 1
Length of EVEN-EVEN language is _________
Select correct option:
radioBtn0
Even
radioBtn1
Odd
radioBtn2
Sometimes even & sometimes odd
radioBtn3
Such language doesn’t exist
Question # 4 of 10 ( Start time: 11:16:41 PM ) Total Marks: 1
If r1 = (aa + bb) and r2 = (a + b) then the language (aa + bb)(a + b) will be generated by
Question # 5 of 10 ( Start time: 11:17:26 PM ) Total Marks: 1
If S = {aa, bb}, then S* will not contain
Aabbaa
Bbaabbbb
Aaabbb
aabbaaaa
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Question # 6 of 10 ( Start time: 11:18:55 PM ) Total Marks: 1
Formal is also known as _________
Syntactic language
Semantic language
Informal language
None of these
Question # 7 of 10 ( Start time: 11:20:15 PM ) Total Marks: 1
In an FA, when there is no path starting from initial state and ending in final state then
that FA
accept null string
accept all strings
accept all non empty strings
does not accept any string
Question # 9 of 10 ( Start time: 11:22:33 PM ) Total Marks: 1
FA of EVEN language shows null string when
Initial state is final as well
EVEN does not accept null
One state is declared null
None of the these
Question No: 1
( Marks: 1 ) - Please choose one
If r1 = (aa + bb) and r2 = ( a + b) then the language (aa + bb)(a + b) will be generated by
► (r1)(r2)
*► (r1 + r2)
► (r2)(r1)
► (r1)*
Question No: 2
( Marks: 1 ) - Please choose one
“One language can be expressed by more than one FA”. This statement is ______
* ► True
► False
► Some times true & sometimes false
► None of these
Question No: 3
( Marks: 1 ) - Please choose one
Who did not invent the Turing machine?
► Alan Turing
*► A. M. Turing
► Turing
► None of these
Question No: 4
( Marks: 1 )- Please choose one
Which statement is true?
*► The tape of turing machine is infinite.
► The tape of turing machine is finite.
► The tape of turing machine is infinite when the language is regular
► The tape of turing machine is finite when the language is nonregular.
Question No: 5
( Marks: 1 ) - Please choose one
A regular language:
► Must be finite
► Must be infinite
► Can be finite or infinite
► Must be finite and cannot be infinite
Question No: 6
( Marks: 1 ) - Please choose one
Every regular expression can be expressed as CFG but every CFG cannot be expressed as
a regular expression. This statement is:
► Depends on the language
► None of the given options
*► True
► False
Question No: 7
( Marks: 1 ) - Please choose one
Above given FA corresponds RE r. then FA corresponding to r* will be
This statement is
*► True
► False
► Depends on language
► None of these
Question No: 8
( Marks: 1 ) - Please choose one
Consider the language L of strings, defined over Σ = {a,b}, ending in a
► There are finite many classes generated by L, so L is regular
*► There are infinite many classes generated by L, so L is regular
► There are finite many classes generated by L, so L is non-regular
► There are infinite many classes generated by L, so L is non-regular
Question No: 9
( Marks: 1 ) - Please choose one
Above given TG has _____________ RE.
► (aa+aa+(ab+ab)(aa+ab)*(ab+ba))*
*► (aa+bb+(ab+ba)(aa+bb)*(ab+ba))*
► (aa+bb+(ab+ba)(aa+bb)(ab+ba))*
► None of these
Question No: 10
( Marks: 1 ) - Please choose one
The word ‘formal’ in formal languages means
*► The symbols used have well defined meaning
► They are unnecessary, in reality
► Only the form of the string of symbols is significant
► None of these
Question No: 11
( Marks: 1 ) - Please choose one
Let A = {0, 1}. The number of possible strings of length ‘n’ that can be formed by the
elements of the set A is
► n!
*► n2
► nm
► 2n
Question No: 12
( Marks: 1 ) - Please choose one
Choose the correct statement.
► A Mealy machine generates no language as such
► A Moore machine generates no language as such
*► A Mealy machine has no terminal state
► All of these
Question No: 13
( Marks: 1 ) - Please choose one
TM is more powerful than FSM because
► The tape movement is confined to one direction
*► It has no finite state control
► It has the capability to remember arbitrary long sequences of input symbols
► None of these
Question No: 14
( Marks: 1 ) - Please choose one
If L1 and L2 are expressed by regular expressions r1 and r2, respectively then the
language expressed by r1 + r2 will be _________
* ► Regular
► Ir-regular
► Can’t be decided
► Another Language which is not listed here
Question No: 15
( Marks: 1 ) - Please choose one
Like TG, a PDA can also be non-deterministic
► True
*► False
Question No: 16
( Marks: 1 ) - Please choose one
The above machine is a/anTG ___________
► Finite Automata
*► Turing machine
► FA
► TG
Question No: 17
( Marks: 1 ) - Please choose one
The language of all words (made up of a’s and b’s) with at least two a’s can not be
described by the regular expression.
► a(a+b)*a(a+b)*(a+b)*ab*
► (a+b)* ab* a(a+b)*
► b*ab* a(a+b)*
► none of these
Question No: 18
( Marks: 1 ) - Please choose one
In FA, if one enters in a specific state but there is no way to leave it, then that specific
state is called
*► Dead State
► Waste Basket
► Davey John Locker
► All of these
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Question No: 19
( Marks: 1 ) - Please choose one
If L is a regular language then, Lc is also a _____ language.
*► Regular
► Non-regular
► Regular but finite
► None of the given
Question No: 20
( Marks: 1 ) - Please choose one
In CFG, the symbols that can’t be replaced by anything are called___
► Terminal
► Non-Terminal
*► Production
► All of given
Question No: 21
( Marks: 1 ) - Please choose one
Which of the following is NOT a regular language?
► String of 0’s whose length is a perfect squere
*► Set of all palindromes made up of 0’s and 1’s
► String of 0’s whose length is a prime number
► All of the given options
Question No: 22
( Marks: 1 ) - Please choose one
Choose the incorrect (FALSE) statement.
► A Mealy machine generates no language as such
► A Mealy machine has no terminal state
*► For a given input string, length of the output string generated by a Moore machine is
not more than the length of the output string generated by that of a Mealy machine
► All of these
Question No: 23
( Marks: 1 ) - Please choose one
Pumping lemma is generally used to prove that:
► A given language is infinite
*► A given language is not regular
► Whether two given regular expressions of a regular language are equivalent or not
► None of these
Question No: 24
( Marks: 1 ) - Please choose one
Which of the following is a regular language?
► String of odd number of zeroes
► Set of all palindromes made up of 0’s and 1’s
*► String of 0’s whose length is a prime number
► All of these
Question No: 25
( Marks: 1 ) - Please choose one
Choose the incorrect statement:
► (a+b)*aa(a+b)* generates Regular language.
► A language consisting of all strings over ∑={a,b} having equal number of a’s and b’s
is a regular language
► Every language that can be expressed by FA can also be expressed by RE
► None of these
MIDTERM EXAMINATION
Spring 2009
CS402- Theory of Automata (Session - 1)
Question No: 1 ( Marks: 1 ) - Please choose one
Alphabet S = {a,bc,cc} has number of letters.
One
Two
Three
Four
Question No: 2 ( Marks: 1 ) - Please choose one
In which of the following language Rev(s)=s
EQUAL
INTEGER
PALINDROME
FACTORIAL
Question No: 3 ( Marks: 1 ) - Please choose one
If S = {ab, bb}, then S* will not contain
abbbab
bbba
bbbbab
ababbb
Question No: 4 ( Marks: 1 ) - Please choose one
a,b
1– 2 +
a,b
Above given FA generates the language having strings of
ODD length
EVEN length
Equal number of a’s and b’s
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
a+b a+b
- aa+bb +
Above given GTG accepts the language in which strings
Contains double a or double b
Contains both a and double b
Depends on the alphabet
None of these
Question No: 6 ( Marks: 1 ) - Please choose one
aa+bb
3- 1
ab+b
a
ab+ba
aa+bb
2
4+
If above given TG
is drawn like
aa+b
b
31X
4
Then what will be
written in place of
X.
(ab+ba)(aa+
bb)(ba+ab)
(ab+ba)(aa+
bb)(ab+ba)
(ab+ba)(aa+
bb)*(ab+ba)
(ab+ba)(aa+
bb)(ab+ba)*
Question No: 7 (
Marks: 1 ) - Please
choose one
FA3 expresses
r1r2. Then initial
state of FA3 will
consist of
Initial state
of FA2
Initial state
of FA1
Initial states
of both FA1 & FA2
Depends on FA’s
Question No: 8 ( Marks: 1 ) - Please choose one
FA3 expresses r1r2. Then
there will be at least one final
state of FA3 that consist of final
state of FA1 and initial state of
FA2.
True
False
Depends on language
None of these
Question No: 9 ( Marks: 1 ) - Please choose one
Two machines are said to be
equivalent if they print the
same output string when the
different input string is run on
them
True
False
Depends on language
May be or may not be
Above given FA accepts strings defined over S={a , b}
All
Some
All but not null
None of these
Question No: 1 ( Marks: 1 ) - Please choose one
Length of null string is
Always not equal to 0
Always equal to 0
It has variable length
All are true
Question No: 2 ( Marks: 1 ) - Please choose one
If an alphabet has n number of letter, then number of strings of length m will be
n+m
(n)(m)
mn
nm
Question No: 3 ( Marks: 1 ) - Please choose one
Languages generated by kleene star are always ______________.
Finite
Infinite
Sometimes finite & sometimes infinite
None of the these
Question No: 4 ( Marks: 1 ) - Please choose one
“Every finite language can be expressed by FA”. This statement is __________.
True
False
Depends on language
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
In FA, if one enters in a specific state but there is no way to leave it, then that specific
state is called
Dead States
Waste Baskets
Davey John Lockers
All of these
Question No: 6 ( Marks: 1 ) - Please choose one
In TG there may exist no paths for certain string.
True
False
Depends on the language
None of these
Question No: 7 ( Marks: 1 ) - Please choose one
In GTG’s there may exist no path for a certain string.
True
False
Depends on alphabet
None of these
Question No: 8 ( Marks: 1 ) - Please choose one
In drawing FA3 (which is equal to FA1 + FA2), a state will be declared final if
States of both FA’s are final
At least one state is final
Depends on language
None of the given
Question No: 9 ( Marks: 1 ) - Please choose one
a
^
1-
4+
b
5
a
a
a
^, b
a
2
3
Above given structure is an ________.
FA
NFA
NFA -^
TG
Question No: 10 ( Marks: 1 ) - Please choose one
b
15+
a 4+ b
a
a,b
a, b 2
3
Above given TG represents the language____
Begins and ends with same letters
Begins and ends with different letters
Begins with a
None of these
Question No: 11 ( Marks: 1 ) - Please choose one
In TG, there may be a transition for null string.
True
False
Can’t show transition for string
None of these
Question No: 12 ( Marks: 1 ) - Please choose one
The _______ machine helps in building a machine that can perform the addition
of binary numbers.
Incrementing
Complementing
Decrementing
None of the given
Question No: 13 ( Marks: 1 ) - Please choose one GTG can have _____________ initial
state.
Zero
One
More than One
One OR more than One
Question No: 14 ( Marks: 1 ) - Please choose one
One FA has n states and m letters in the alphabet. Then FA will have _____
number of transitions in the diagram.
(n)+(m)
(m)(n) OR (n)(m)
None of the given options
(m)-(n)
Question No: 15 ( Marks: 1 ) - Please choose one
If L1 and L2 are expressed by regular expressions r1 and r2, respectively then the
language expressed by r1 + r2 will be _________
Regular
Ir-regular
Can’t be decided
Another Language which is not listed here
Question No: 16 ( Marks: 1 ) - Please choose one
Which statement is true?
All words are strings
All strings are words
Both are always same
None of these
Question No: 6 ( Marks: 1 ) - Please choose one
According to 3rd part of the Kleene’s theorem, If a language can be accepted by
an RE then it can be accepted by a as well
TG
FA
TG and FA
None of these
Question No: 7 ( Marks: 1 ) - Please choose one
r1
r2
…. 5 ….
…
rn .
r1+r2 + …
…. 5 ….
+rn
Above given GTG’s are
Equivalent
Non-equivalent
Non-valid
What is meant by tokenizing a string?
Question No: 19 ( Marks: 2 )
Define the language for the following NFA also write the regular expression for the
language?
a,b
1- a
2 a 3+
a,b
Question No: 20 ( Marks: 3 )
Describe the method of NFA corresponding to Concatenation of FAs.
Question No: 21 ( Marks: 5 )
(i) When asked to give a recursive definition for the language PALINDROM over the
alphabet S = {a, b}, a student wrote:
Rule 1 a and b are in PALINDROM.
Rule 2 If x is in PALINDROM, then so are axa and bxb
Unfortunately all the words in the language defined above have an odd length and so it is
not all of PALINDROM. Fix this problem.
(ii) Give a recursive definition for the language EVENPALINDROM of all palindromes
of even length
Question No: 22 ( Marks: 10 )
What do you mean by “bypass and state elimination” Also reduce the following TG by
eliminating state 3. (Draw reduced TG)
MIDTERM EXAMINATION
Spring 2009
CS402- Theory of Automata (Session - 3)
Question No: 1 ( Marks: 1 ) - Please choose one
If r1 and r2 are regular expressions then which of the following is not regular
expression.
r1 = r2
r1r2
r1*
r1 – r2
Question No: 2 ( Marks: 1 ) - Please choose one
Which of the following is not a word of language EQUAL?
aaabbb
abbbabaa
abababa
bbbaaa
Question No: 3 ( Marks: 1 ) - Please choose one
If S = {aa, bb}, then S* will not contain..
aabbaa
bbaabbbb
aaabbb
aabbbb
Question No: 4 ( Marks: 1 ) - Please choose one
One language can be represented by more than one RE” this statement is
False
True
Can’t be assumed
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
“Every Infinite language is regular” this statement is
True
False
Can’t be supposed
None of these
Question No: 6 ( Marks: 1 ) - Please choose one
PALINDROME can be defined by more than one regular language
True
False
By only one RE
Some times By only one RE and Some times False
Question No: 7 ( Marks: 1 ) - Please choose one
a,b
1
a,b
2+
Above given FA can be expressed as
a* + b*
(ab + ba)*
None of these
Above given TG has RE.
(aa+bb+(ab+ba)(aa+bb)(ab+ba))*
(aa+bb+(ab+ba)(aa+bb)*(ab+ba))*
(aa+ba+(bb+ba)(ab+bb)(ab+aa))*
(ab+ba+(ab+ba)(aa+bb)(ab+ba))*
Question No: 17 ( Marks: 1 )
How can we say that two REs are equal?
Question No: 18 ( Marks: 1 )
What is meant by Kleene star closure of a language?
Question No: 19 ( Marks: 2 )
What the Pumping lemma II says about length(x) + length(y) must be:
Question No: 20 ( Marks: 3 )
Consider the language S*, where S = {ab, ba}, Can any
word in this language contain the substrings aaa or bbb?
Why or why not?
Question No: 21 ( Marks: 5 )
Give the transition table of an FA3 corresponding to
FA1+FA2, where FA1, FA2 are given below.
FA1
FA2
Question No: 22 ( Marks: 10 )
What is meant by nondeterminism? Draw the TG for the following RE
(aa)*b(b*+( (aa)+b)*) bb.
CS402Theory of
Automata
(Session - 3)
Question No: 1 ( Marks: 1 ) - Please choose one
S = {baa, ab}, then S* will not contain
abbaab
abab
baabaa
abbaa
Question No: 2 ( Marks: 1 ) - Please choose one
1*(1 + ) = 1* this statement is
True
False
Sometimes true & sometimes false
None of these
Question No: 3 ( Marks: 1 ) - Please choose one
One language can be represented by more than one RE” this statement is
False
True
Can’t be assumed
None of these
Question No: 4 ( Marks: 1 ) - Please choose one
a(a+b)*a+b(a+b)*b is RE for the language defined over S={a,b} having words
beginning
and ending with same letters
True
False
Such a language is not regular
None of these
Question No: 5 ( Marks: 1 ) - Please choose one
baa
–+
b
Above given FA can be expressed by
(a + b)*a
(a + b)*b
a (a + b)*
b (a + b)*
Question No: 6 ( Marks: 1 ) - Please choose one
If a language has RE, then that language can be expressed through TG.
True
False
Depends on language
None of these
Question No: 7 ( Marks: 1 ) - Please choose one
In TG there may exist no paths for certain string.
True
False
Depends on the language
None of these
Question No: 9 ( Marks: 1 ) - Please choose one
FA1 corresponds to r*, then FA1 must accept
string.
Every
Null
Odd length
Even length
Question No: 10 ( Marks: 1 ) - Please choose one
In NFA, there may be more than one transition for
certain letters and there may not be any transition
for certain letters. This statement is .
False
True
Depends on language
None of the given
Question No: 11 ( Marks: 1 ) - Please choose one
a,b
b
–+
Above given TG accepts the language in which all strings
Ends in b
Begins with b
Ends and begins with b
None of the given
Question No: 1 ( Marks: 1 ) - Please choose one
Σ={a,Aa,Abb}, then string aAaAbbAa has ________ length.
► One
► Two
► Three
► Four
Question No: 2 ( Marks: 1 ) - Please choose one
Languages generated by kleene star are always ______________.
► Finite
► Infinite
► Sometimes finite & sometimes infinite
► None of the these
Question No: 3 ( Marks: 1 ) - Please choose one
Let
S = {aa, bb} be a set of strings then s* will have
►Λ
► abba
► aabbbaa
► bbaab
Question No: 4 ( Marks: 1 ) - Please choose one
If r1
= (aa + bb) and r2 = ( a + b) then the language (aa + bb)* will be generated by
► (r1)(r2)
► (r1 + r2)
► (r2)*
► (r1)*
Question No: 5 ( Marks: 1 ) - Please choose one
y
a, b
x±
a, b
Above given FA can be represented by
► ((a+ b) (a + b))*
► (a + b)(a + b)*
► (a + b)(a + b)
► (a + b)*(a + b)*
Question No: 6 ( Marks: 1 ) - Please choose one
a,b
2+
1± a,b
Above given FA accepts ___________ strings defined over Σ={a , b}
► All
► Some
► All but not null
► None of these
Question No: 7 ( Marks: 1 ) - Please choose one
If a
language can be expressed through FA, then it can also be expressed through TG.
► True
► False
► Depends on language
► None of the above
Question No: 8 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given TG has ____________________ RE.
► a+b+a(a + b)*a + b(a + b)*b
► a(a + b)*a + b(a + b)*b
► both are given
► none of the given
Question No: 9 ( Marks: 1 ) - Please choose one
b
b
3+
a
1a
aa
a
4+
b
2.b
b
ba
56
Above given FA accepts the language in which strings
► Begins with and ends in same letter
► Begins with and ends in different letter
► Has length more than 2
► None of the given
Question No: 10 ( Marks: 1 ) - Please choose one
GTG can have _______________ final state.
►0
►1
► More than 1
► All of the given
Question No: 11 ( Marks: 1 ) - Please choose one
In
GTG, if a state has more than one incoming transitions from a state. Then all those
incoming
transitions can be reduced to one transition using _____________ sign
►►+
►*
► None of the given
Question No: 12 ( Marks: 1 ) - Please choose one
aa+bb
ab+ba
ab+ba
aa+bb
Λ
4+
3- 1 2
Λ
If above given TG is drawn like
aa+bb
Λ
4
31
Λ
X
Then what will be written in place of X.
► (ab+ba)(aa+bb)(ba+ab)
► (ab+ba)(aa+bb)(ab+ba)
► (ab+ba)(aa+bb)*(ab+ba)
► (ab+ba)(aa+bb)(ab+ba)*
Question No: 13 ( Marks: 1 ) - Please choose one
“One language can be expressed by more than one NFA”. This statement is
______________.
► False
► True
► Depends on NFA
► None of the given
Question No: 14 ( Marks: 1 ) - Please choose one
a
^
1-
4+
b5
aa
a
^, b
a
2
3
Above given structure is an ________.
► FA
► NFA
► NFA -^
► TG
Question No: 15 ( Marks: 1 ) - Please choose one
One
FA has 3 states and 2 letters in the alphabet. Then FA will have ___________
number of
transitions in the diagram
►4
►5
►7
►6
Question No: 16 ( Marks: 1 ) - Please choose one
aa
b
bb
a
123+
4+
b
a
Above given two TG’s are _______________.
► Equivalent
► None-equivalent
► Not valid
► None of the given
Question No: 17 ( Marks: 1 )
What do you mean by dead state?
Question No: 18 ( Marks: 1 )
Define empty or null strings?
Question No: 19 ( Marks: 2 )
Write strings that ends on "a" and strings containing exactly one "a". over Σ= {a, b}
Question No: 20 ( Marks: 3 )
Let S be all string of a’s and b’s with odd length. What is S*?
Question No: 21 ( Marks: 5 )
Give the transition table of an FA3 corresponding to FA1+FA2, where FA1, FA2 are
given below.
FA1
FA2
Question No: 22 ( Marks: 10 )
Give the regular expression and draw the GTG for the following language.
Language L of strings, defined over Σ = {a, b}, beginning with and ending in same
letters.
In which of the following language Rev(s)=s
1. Equal
2. Integer
3. Palindrome
4. Factorial
Q1
A DFA with n states must accept at least one string of length greater than n.
Choices:
1. True
2. False
Q2
FA corresponding to an NFA can be built by introducing a state corresponding to the
combination of states, for a letter having
Choices:
1. no transition at certain state
2. one transition at certain state
3. more than one transitions at certain state
4. none of the given options
Q3
Which of the following statement is NOT true?
Choices:
1. FA can be considered to be an NFA
2. FA can be considered to be an NFA with null string
3. NFA can be considered to be an TG
4. TG can be considered to be an NFA
Q4
For every three regular expressions R, S, and T, the languages denoted by R(S U T) and
(RS) U
(RT) are the same.
Choices:
1. True
2. False
Q5
Does the empty string match the regular expression |y+a|?
Choices:
1. Yes
2. No
Q6
If an FA already accepts the language expressed by the closure of certain RE, then the
given FA
is the required FA.
Choices:
1. True
2. False
Q7
Which of the following statement is true about NFA with Null String?
Choices:
1. Infinite states
2. Infinite set of letters
3. Infinite set of transitions
4. Transition of null string is allowed at any stage
Q8
If R is a regular language and L is some language, and L U R is a regular language, then
L must
be a regular language.
Choices:
1. True
2. False
Q9
FA corresponding to an NFA can be built by introducing an empty state for a letter
having
Choices:
1. no transition at certain state
2. one transition at certain state
3. two transition at certain state
4. more than two transitions at certain state
Q10
Let FA3 be an FA corresponding to FA1FA2, then the initial state of FA3 must
correspond to the
initial state of
Choices:
1. FA1 only
2. FA2 only
3. FA1 or FA2
4. FA1 and FA2
If an FA accept a word then there must exist a path from
1. Initial to final state.
2. Initial to each state
3. Initial to each state but not to final state.
4. Initial to final state by traversing each state
If an FA has N state then it must accept the word of length
1. n-1
2. state
3. transition
4. input tape
The part of an FA, where the input string is placed before it is run, is called _______
1. state
2. transition
3. input tape
4. output tape
The complement of a regular language is also a regular
1. True
2. False
A PDA is not in conversion form if ___________
1. There are more than one ACCEPT states
2. There are more than one REJECT states
3. Every READ or HERE is followed immediately by a put
4. All of the given options
In conversion form of PDA there is no……… state
1. Push
2. Read
Consider the following production (of a CFG): S->XYZ Here ______ is left most nonterminal
in working string. Note: S, X, Y and Z are all non-terminals
1. S
2. X
3. Y
4. Z
Which of the following states is not part of PDA
1. Start
2. Accept
3. Write
4. reject
The tree which produced all the strings of a language is called
1. Derivation tree
2. Ambiguous tree
3. Total language tree
4. Non-Ambiguous tree
None of the given
Question No: 8 ( Marks: 1
) - Please choose one
If FA1
accepts
no string
and FA2
accepts
many
strings,
then FA1
+ FA2
will be
equal to
FA1
FA2
May be both
None of the given
Question No: 9 ( Marks: 1 ) - Please
choose one
abb
-+
a
a, b
-b+
Above given NFA and FA generate same language.
True
False
FA & NFA can’t be equivalent
None of these
Question No: 10 ( Marks: 1 ) - Please choose one
-a+
Above given structure is a
FA
TG
NFA
FA and NFA
Question No: 11 ( Marks: 1 ) - Please choose one
2a4
a,b a
a
a,b
1– 6+
bb
3b5
a,b
aaa,bbb
a,b
+
Above given TG’s are .
Equivalent
Non-equivalent
TG’s are not valid
None of these
Question No: 12 ( Marks: 1 ) - Please choose one
–– a +
––
Above given TG has the RE.
(a + b)*a
+ (a + b)*a
None of these
+ (a + b)*a*
Question No: 13 ( Marks: 1 ) - Please choose one
a
a
–– +
ab
b
b
Above given FA has RE.
(a + b)*a
a(a + b)*
((a + b)*a)*
(a + b)*a & ((a + b)*a)*
Question No: 14 ( Marks: 1 ) - Please choose one
–– b
a,b
+
Above given TG accepts the string.
bb
baba
bbba
all of the given options
Question No: 17 ( Marks: 1 )
What is the difference between Regular Languages and Non Regular Languages?
Question No: 18 ( Marks: 1 )
Question No: 26
( Marks: 1 ) - Please choose one
Left hand side of a production in CFG consists of:
► One terminal
► More than one terminal
► One non-terminal
* ► Terminals and non-terminals