Models of Computation

Outline of the course contents Computation memory CPU

temporary memory input CPU output Program memory

Example: temporary memory input CPU output Program memory compute

temporary memory input CPU output Program memory compute compute

temporary memory input CPU output Program memory compute compute

temporary memory input CPU Program memory output compute compute

Automaton temporary memory Automaton input CPU output Program memory

Automaton temporary memory Automaton input output transition state

Different Kinds of Automata Automata are distinguished by the temporary memory Finite Automata: no temporary memory Pushdown Automata: stack Turing Machines: random access memory

Finite Automaton temporary memory input Finite Automaton output Example: Elevators, Vending Machines (small computing power)

Pushdown Automaton Stack Push, Pop input Pushdown Automaton output Temp. memory Stack Push, Pop input Pushdown Automaton output Example: Compilers for Programming Languages (medium computing power)

Turing Machine Random Access Memory input Turing Machine output Temp. memory Random Access Memory input Turing Machine output Examples: Any Algorithm (highest computing power)

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

Turing Machine is the most powerful computational model known Question: Are there computational problems that a Turing Machine cannot solve? Answer: Yes (unsolvable problems)

Time Complexity of Computational Problems: NP-complete problems Believed to take exponential time to be solved P problems Solved in polynomial time

This Summary is an Online Content from this Book: Michael Sipser, Introduction to the Theory of Computation, 2ndEdition It is edited for Computation Theory Course 6803415-3 by: T.Mariah Sami Khayat Teacher Assistant @ Adam University College For Contacting: mskhayat@uqu.edu.sa Kingdom of Saudi Arabia Ministry of Education Umm AlQura University Adam University College Computer Science Department المملكة العربية السعودية وزارة التعليم جامعة أم القرى الكلية الجامعية أضم قسم الحاسب الآلي