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CSCI-2400

Models of Computation

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Syllabus: tentative class schedule

can be found in course web page

http://www.cs.rpi.edu/~buschc/courses/modcomp/fall2005

Grading: Weekly Homeworks: 34%

3 Exams: 66% (each 22%)

Instructor: Costas Busch

General Info for the Course

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Book: Introduction to the

Theory of Computation

Michael Sipser, 2nd edition

Chapters that will be covered: 1-5,7

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Computation

CPU memory

Outline of the course contents

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CPUinput

output

Program memory

temporary memory

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CPUinput

output

Program memory

temporary memory

3)( xxf !

compute xx

compute

xx

2

Example:

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CPU

input

output

Program memory

temporary memory

3)( xxf !

compute xx

compute

xx

2

2!

x

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CPU

input

output

Program memory

temporary memory 3)( xxf !

compute xx

compute

xx

2

2!

x

42*2 !!z

82*)( !! zxf

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CPU

input

outputProgram memory

temporary memory 3)( xxf !

compute xx

compute

xx

2

2!

x

42*2 !!z

82*)( !! zxf

8)( !xf

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Automaton

CPUinput

output

Program memory

temporary memory

Automaton

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Automaton

input

output

temporary memory

Automaton

state

transition

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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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input

output

temporary memory

FiniteAutomaton

Finite Automaton

Example: Vending Machines

(small computing power)

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input

output

Stack

Pushdown

Automaton

Pushdown Automaton

Example: Compilers for Programming Languages

(medium computing power)

Push, PopTemp.

memory

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input

output

Random Access Memory

Turing

Machine

Turing Machine

Examples: Any Algorithm

(highest computing power)

Temp.memory

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Finite

AutomataPushdownAutomata

TuringMachine

Power of Automata

Less power More power

Solve more

computational problems

Simpleproblems

More complexproblems

Hardestproblems

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Turing Machine is the most powerful

computational model known

Question:A

re there computationalproblems that a Turing Machine

cannot solve?

Answer: Yes (unsolvable problems)

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Time Complexity of Computational Problems:

NP-complete problems

P problems

Believed to take exponential

time to be solved

Solved in polynomial time