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CMPS 3223 Theory of Computation

This chapter discusses decision procedures, nondeterminism, and functions on languages in the context of the theory of computation. Topics include defining problems as languages, determining solutions, the difference between deterministic and nondeterministic programs, and performing functions on languages.

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CMPS 3223 Theory of Computation

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  1. CMPS 3223Theory of Computation Automata, Computability, & Complexity by Elaine Rich ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Slides provided by author Slides edited for use by MSU Department of Computer Science – R. Halverson

  2. Computation Chapter 4

  3. Our Goals • Define a problem as a language • Define program/machine which accepts a string as input & determines if the string is in the language

  4. Three Computational Issues Decision procedures Nondeterminism Functions on functions and programs

  5. 1. Decision Procedures • Decision Problem • Yes or No solution • Algorithm • Detailed process/procedure that accomplishes some task • Decision Procedure • An algorithm that provides a Yes or No solution to a decision problem

  6. 2. Nondeterminism • Deterministic Program • Given a single input, all executions of the program compute the same solution • I.E. We can DETERMINE with certainty what the solution will be. • Nondeterministic Program • Given a single input, different executions of the program may produce different solutions.

  7. How is nondeterminism possible? • You answer this question!!

  8. Nondeterminism This is author’s method of specifying. We will seldom, if ever, use this. 1. choose (action 1;; action 2;; … action n ) 2. choose(x from S: P(x))

  9. Nondeterminism Example Want plane ticket, rental car, train/public transportation for a trip. Is optimal (cheapest/fastest) absolutely necessary?? trip-plan(start, finish) = return (choose( fly-major-airline-and-rent-car(start, finish);; fly-regional-airline-and-rent-car(start, finish);; take-train-and-use-public-transportation (start, finish);; drive(start, finish) ))

  10. Nondeterminism Convert first to second. Is a solution possible? How will you find it? How long will it take?

  11. 3. Functions on Languages • Given a language, perform some function on the language to create a new language • Concatenation, Repetition, Union, Intersection • Can define many others • E.G. Chop = all odd strings of a language with the middle character “chopped” out

  12. Homework Chapter 4 None

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