CS-300
Theory of Computation
2nd Sem 2017
Lecture 1
1
General Info for the Course
Instructor: Dr.Mohammad El-Bashir
Syllabus: tentative class schedule
can be found in course web page
Book: Introduction to the
Theory of Computation
Michael Sipser, 3rd edition
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Lecture 1
2
Outline of the course contents
Computation
CPU
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Lecture 1
memory
3
temporary memory
input
CPU
output
Program memory
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4
Example:
f ( x)  x
3
temporary memory
input
CPU
output
Program memory
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compute
xx
compute
x x
2
Lecture 1
5
f ( x)  x
temporary memory
3
input
x2
CPU
output
Program memory
2nd Sem 2017
compute
xx
compute
x x
2
Lecture 1
6
temporary memory
z  2*2  4
f ( x)  z * 2  8
f ( x)  x
3
input
x2
CPU
output
Program memory
2nd Sem 2017
compute
xx
compute
x x
2
Lecture 1
7
temporary memory
z  2*2  4
f ( x)  z * 2  8
f ( x)  x
3
input
x2
CPU
f ( x)  8
Program memory
2nd Sem 2017
compute
xx
compute
x x
output
2
Lecture 1
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Automaton
temporary memory
Automaton
input
CPU
output
Program memory
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Automaton
temporary memory
Automaton
input
output
transition
state
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Different Kinds of Automata
Automata are distinguished by the temporary memory
• Finite Automata:
no temporary memory
• Pushdown Automata:
stack
• Turing Machines:
random access memory
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Finite Automaton
temporary memory
input
Finite
Automaton
output
Example: Elevators, Vending Machines
(small computing power)
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Pushdown Automaton
Temp.
memory
Stack
Push, Pop
input
Pushdown
Automaton
output
Example: Compilers for Programming Languages
(medium computing power)
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Turing Machine
Temp.
memory
Random Access Memory
input
Turing
Machine
output
Examples: Any Algorithm
(highest computing power)
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Power of Automata
Simple
problems
More complex
problems
Hardest
problems
Finite
Pushdown
Automata
Turing
Automata
Machine
Less power
More power
Solve more
computational problems
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15
Turing Machine is the most powerful
computational model known
Question: Are there computational
problems that a Turing Machine
cannot solve?
Answer: Yes
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(unsolvable problems)
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16
Time Complexity of Computational Problems:
NP-complete problems
Believed to take exponential
time to be solved
P problems
Solved in polynomial time
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