1. Fall 2006Costas Busch - RPI1 CSCI-2400 Models of Computation

2. Fall 2006Costas Busch - RPI2 Syllabus: tentative class schedule can be found in course web page http://www.cs.rpi.edu/~moorthy/Courses/CSCI2400 Instructor: Moorthy General Info for the Course Book: Introduction to the Theory of Computation Michael Sipser, 2 nd edition

3. Fall 2006Costas Busch - RPI3 Computation CPU memory Outline of the course contents

4. Fall 2006Costas Busch - RPI4 CPU input output Program memory temporary memory

5. Fall 2006Costas Busch - RPI5 CPU input output Program memory temporary memory compute Example:

6. Fall 2006Costas Busch - RPI6 CPU input output Program memory temporary memory compute

7. Fall 2006Costas Busch - RPI7 CPU input output Program memory temporary memory compute

8. Fall 2006Costas Busch - RPI8 CPU input output Program memory temporary memory compute

9. Fall 2006Costas Busch - RPI9 Automaton CPU input output Program memory temporary memory Automaton

10. Fall 2006Costas Busch - RPI10 Automaton input output temporary memory Automaton state transition

11. Fall 2006Costas Busch - RPI11 Different Kinds of Automata Automata are distinguished by the temporary memory Finite Automata: no temporary memory Pushdown Automata: stack Turing Machines: random access memory

12. Fall 2006Costas Busch - RPI12 input output temporary memory Finite Automaton Example: Elevators, Vending Machines (small computing power)

13. Fall 2006Costas Busch - RPI13 input output Stack Pushdown Automaton Pushdown Automaton Example: Compilers for Programming Languages (medium computing power) Push, Pop Temp. memory

14. Fall 2006Costas Busch - RPI14 input output Random Access Memory Turing Machine Turing Machine Examples: Any Algorithm (highest computing power) Temp. memory

15. Fall 2006Costas Busch - RPI15 Finite Automata Pushdown Automata Turing Machine Power of Automata Less powerMore power Solve more computational problems Simple problems More complex problems Hardest problems

16. Fall 2006Costas Busch - RPI16 Turing Machine is the most powerful computational model known Question: Are there computational problems that a Turing Machine cannot solve? Answer: Yes(unsolvable problems)

17. Fall 2006Costas Busch - RPI17 Time Complexity of Computational Problems: NP-complete problems P problems Believed to take exponential time to be solved Solved in polynomial time