Fall 2005Costas Busch - RPI1 CSCI-2400 Models of Computation

Fall 2005Costas Busch - RPI2 Syllabus: tentative class schedule can be found in course web page Grading: Weekly Homeworks: 34% 3 Exams: 66% (each 22%) Instructor: Costas Busch General Info for the Course

Fall 2005Costas Busch - RPI3 Book: Introduction to the Theory of Computation Michael Sipser, 2 nd edition Chapters that will be covered: 1-5,7

Fall 2005Costas Busch - RPI4 Computation CPU memory Outline of the course contents

Fall 2005Costas Busch - RPI5 CPU input output Program memory temporary memory

Fall 2005Costas Busch - RPI6 CPU input output Program memory temporary memory compute Example:

Fall 2005Costas Busch - RPI7 CPU input output Program memory temporary memory compute

Fall 2005Costas Busch - RPI8 CPU input output Program memory temporary memory compute

Fall 2005Costas Busch - RPI9 CPU input output Program memory temporary memory compute

Fall 2005Costas Busch - RPI10 Automaton CPU input output Program memory temporary memory Automaton

Fall 2005Costas Busch - RPI11 Automaton input output temporary memory Automaton state transition

Fall 2005Costas Busch - RPI12 Different Kinds of Automata Automata are distinguished by the temporary memory Finite Automata: no temporary memory Pushdown Automata: stack Turing Machines: random access memory

Fall 2005Costas Busch - RPI13 input output temporary memory Finite Automaton Example: Vending Machines (small computing power)

Fall 2005Costas Busch - RPI14 input output Stack Pushdown Automaton Pushdown Automaton Example: Compilers for Programming Languages (medium computing power) Push, Pop Temp. memory

Fall 2005Costas Busch - RPI15 input output Random Access Memory Turing Machine Turing Machine Examples: Any Algorithm (highest computing power) Temp. memory

Fall 2005Costas Busch - RPI16 Finite Automata Pushdown Automata Turing Machine Power of Automata Less powerMore power Solve more computational problems Simple problems More complex problems Hardest problems

Fall 2005Costas Busch - RPI17 Turing Machine is the most powerful computational model known Question: Are there computational problems that a Turing Machine cannot solve? Answer: Yes(unsolvable problems)

Fall 2005Costas Busch - RPI18 Time Complexity of Computational Problems: NP-complete problems P problems Believed to take exponential time to be solved Solved in polynomial time