CSC4890 Introduction to the Theory of Computation Costas

General Info about Course Instructor: Konstantin (Costas) Busch Books • Introduction to the Theory

Course Goals Provide computation Models Analyze power of Models Answer Intractability questions: What computational

A widely accepted model of computation CPU Costas Busch - LSU memory 4

The different components of memory temporary memory input CPU output Program memory Costas Busch

Example: temporary memory input CPU output Program memory compute Costas Busch - LSU 6

temporary memory input CPU output Program memory compute Costas Busch - LSU 7

temporary memory input CPU output Program memory compute Costas Busch - LSU 8

temporary memory input CPU Program memory output compute Costas Busch - LSU 9

Automaton temporary memory Automaton input CPU output Program memory Costas Busch - LSU 10

Automaton temporary memory Automaton input output transition state CPU+Program. Mem = States + Transitions

Different Kinds of Automata are distinguished by the temporary memory • Finite Automata: no

Memory affects computational power: More flexible memory results to The solution of more computational

Finite Automaton temporary memory input Finite Automaton output Example: Elevators, Vending Machines, Lexical Analyzers

Pushdown Automaton Temp. memory Stack Push, Pop input Pushdown Automaton output Example: Parsers for

Turing Machine Temp. memory Random Access Memory input Turing Machine output Examples: Any Algorithm

Power of Automata Simple problems More complex problems Hardest problems Finite Pushdown Automata Turing

Turing Machine is the most powerful known computational model Question: can Turing Machines solve

Time Complexity of Computational Problems: P problems: (Polynomial time problems) Solved in polynomial time

Slides: 19

Download presentation

CSC-4890 Introduction to the Theory of Computation Costas Busch - LSU 1

General Info about Course Instructor: Konstantin (Costas) Busch Books • Introduction to the Theory of Computation, Michael Sipser • An Introduction to Formal Languages and Automata, Peter Linz Costas Busch - LSU 2

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? Costas Busch - LSU 3

A widely accepted model of computation CPU Costas Busch - LSU memory 4

The different components of memory temporary memory input CPU output Program memory Costas Busch - LSU 5

Example: temporary memory input CPU output Program memory compute Costas Busch - LSU 6

temporary memory input CPU output Program memory compute Costas Busch - LSU 7

temporary memory input CPU output Program memory compute Costas Busch - LSU 8

temporary memory input CPU Program memory output compute Costas Busch - LSU 9

Automaton temporary memory Automaton input CPU output Program memory Costas Busch - LSU 10

Automaton temporary memory Automaton input output transition state CPU+Program. Mem = States + Transitions Costas Busch - LSU 11

Different Kinds of Automata are distinguished by the temporary memory • Finite Automata: no temporary memory • Pushdown Automata: stack • Turing Machines: random access memory Costas Busch - LSU 12

Memory affects computational power: More flexible memory results to The solution of more computational problems Costas Busch - LSU 13

Finite Automaton temporary memory input Finite Automaton output Example: Elevators, Vending Machines, Lexical Analyzers (small computing power) Costas Busch - LSU 14

Pushdown Automaton Temp. memory Stack Push, Pop input Pushdown Automaton output Example: Parsers for Programming Languages (medium computing power) Costas Busch - LSU 15

Turing Machine Temp. memory Random Access Memory input Turing Machine output Examples: Any Algorithm (highest known computing power) Costas Busch - LSU 16

Power of Automata Simple problems More complex problems Hardest problems Finite Pushdown Automata Turing Automata Machine Less power More power Solve more computational problems Costas Busch - LSU 17

Turing Machine is the most powerful known computational model Question: can Turing Machines solve all computational problems? Answer: NO (there are unsolvable problems) Costas Busch - LSU 18

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 Costas Busch - LSU 19