Math 156 – Fall 2011
1/2
Problem Sets Between Test 2 and Test 3
Only turn in problems that are not bracketed. Bracketed problems are additional problems you can look
at. Round brackets indicate problems that may help you with problems that are assigned; square brackets are
additional problems on material that you should know, but you are not required to write up solutions; curly
brackets are truly optional and may contain extra nuggets that you will not be required to know but may be
interested in.
Additional assignments will be filled in over time.
notation
meaning
unbracketed
assigned problem – turn these in for grading
()
helper/warm-up problem
[]
additional problems (you are responsible for content, but don’t turn them in)
{}
covers optional material
PS
Due
Source
16
Tue 11/8
Rosen 8.3
(7) 8 (9) 10
17
Fri 11/11
Rosen 8.3
35 37
Rosen 8.SE
10 21
Rosen 13.5
1–3
Rosen 13.5
7
18
Tue 11/15
Problems
solve
22
√
tracing TM
0→1
9
0→1
10
11 → 00
25
min
Notes:
• Each of these must be done using Eliot Eshelman’s Turing
Machine simulator.
• Your machines may use a 1-way or a 2-way infinite tape
(your choice).
• You may only use 1 tape.
• Numbers are to be coded in unary. Multiple-input machines
separate the inputs with an asterisk. (See page 892 for details and examples.)
• All computations must be clean. That is, your machine
must return to the leftmost non-blank cell of tape and end
in an appropriate state.
• Save
your
Turing
machine
to
a
file
with
the names Rosen7.tm,
Rosen9.tm,
etc.
in
/home/math156/current/*/PS18/ on the ulab machines
as you do in your CS courses.
Created November 28, 2011 — See web site for most current version.
Math 156 – Fall 2011
2/2
PS
Due
Source
19
Fri 11/18
Rosen 13.5
Problems
16
02n 1n
20
mod 3
Busy TM Challenge. Your challenge here is to write a TM
that has a single 2-way infinite tape, tape alphabet {1, B}, and a
fixed number of states, so that when started on a blank it runs
for a while and halts with as many consecutive 1’s on the tape as
possible. This computation does not need to be clean.
For this problem you will write four TMs called busy2.tm,
busy3.tm, busy4.tm, and busy5.tm. These machines will have
2, 3, 4, and 5 states respectively.
• Write busy2.tm so that it outputs at least 4 consecutive 1’s.
• See how many consecutive 1’s you can get with your machines busy3.tm, busy4.tm, and busy5.tm.
Your score will be based on how large the number is.
Save your Turing machines to a files with the names Rosen16.tm,
Rosen20.tm, busy2.tm, busy3.tm, busy4.tm, and busy5.tm. etc.
in /home/math156/current/*/PS19/ on the ulab machines as you
do in your CS courses. Follow the same rules as for PS 18.
20
Tue 11/22
Rosen 13.1
1ad [2] (3) 4 [5] 6a 9 (13) 14bd [15] 19
21
Tue 11/29
Rosen 13.1
20 palindromes 21a union 24ab derivation trees 28 BNF 31ab BNF 34 EBNF
Rosen 13.3
1 notation (9) notation 10 notation (11) DFA trace 12 DFA trace
18–20 DFA language (23) build DFA 24 build DFA 28 build DFA
45–46 NFA language 52 NFA to DFA [52–54] NFA to DFA
**
Rosen 13.4
[23–25]
**
Rosen 8.RQ
[1–2] [6–9]
**
Rosen 8.SE
[1–2] [4–6] [9] [20–21]
**
Rosen 13.RQ
[1–5] [7–19]
**
Rosen 13.SE
[5]
**
ambiguous grammar
[19–20]
types of grammars
NFA to DFA
Created November 28, 2011 — See web site for most current version.