1. Formal Foundations-II [Theory of Automata]
Dr. Malik Jahan Khan
Assistant Professor (Computer Science)

2. Course Organization Text Book: Michael Sipser, “Introduction to
Theory of Computation”, Course Technology, MIT
Weights: Homeworks Formative Quizzes Formative Midterm 15% Final Exam 75%

3. What we will do Automata = abstract computing devices
Turing studied Turing Machines (= computers) before there were any real computers
We will also look at simpler devices than Turing machines (Finite State Automata, Pushdown Automata, ), and specification means, such as grammars and regular expressions.
NP-hardness = what cannot be efficiently computed

4. Course Goals Provide computation Models Analyze power of Models
Answer Intractability questions:
What computational problems
can each model solve?
Answer Time Complexity questions:
How much time we need to
solve the problems?
Prof. Busch - LSU

5. A widely accepted model of computation
memory
CPU
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6. The different components of memory
temporary memory
input
CPU
output
Program memory
Prof. Busch - LSU

7. Example: temporary memory input CPU output Program memory compute
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8. temporary memory input CPU output Program memory compute compute
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9. temporary memory input CPU output Program memory compute compute
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10. temporary memory input CPU Program memory output compute compute
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11. Automaton temporary memory Automaton input CPU output Program memory
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12. Automaton CPU+ProgramMem = States + Transitions temporary memory
input
output
transition
state
CPU+ProgramMem = States + Transitions
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13. Different Kinds of Automata
Automata are distinguished by the temporary memory
Finite Automata: no temporary memory
Pushdown Automata: stack
Turing Machines: random access memory
Prof. Busch - LSU

14. Memory affects computational power:
More flexible memory
results to
The solution of more computational
problems
Prof. Busch - LSU

15. Finite Automaton temporary memory input Finite Automaton output
Example: Elevators, Vending Machines,
Lexical Analyzers
(small computing power)
Prof. Busch - LSU

16. Pushdown Automaton Stack Push, Pop input Pushdown Automaton output
Temp.
memory
Stack
Push, Pop
input
Pushdown
Automaton
output
Example: Parsers for Programming Languages
(medium computing power)
Prof. Busch - LSU

17. Turing Machine Random Access Memory input Turing Machine output
Temp.
memory
Random Access Memory
input
Turing
Machine
output
Examples: Any Algorithm
(highest known computing power)
Prof. Busch - LSU

18. Power of Automata Finite Automata Pushdown Automata Turing Machine
Simple
problems
More complex
problems
Hardest
problems
Finite
Automata
Pushdown
Automata
Turing
Machine
Less power
More power
Solve more
computational problems
Prof. Busch - LSU

19. Turing Machine is the most powerful known computational model
Question: can Turing Machines solve
all computational problems?
Answer: NO
(there are unsolvable problems)
Prof. Busch - LSU

20. Time Complexity of Computational Problems:
P problems:
(Polynomial time problems)
Solved in polynomial time
NP-complete problems:
(Non-deterministic Polynomial time problems)
Believed to take exponential
time to be solved
Prof. Busch - LSU