Module06 - a string over the program alphabet Σ P ={a …...

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1 Module 6 Topics Program behavior problems Input of problem is a program/algorithm Definition of type program Program correctness Testing versus Proving
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2 Number Theory Problems These are problems where we investigate properties of numbers Primality Input: Positive integer n Yes/No Question: Is n a prime number? Divisor Input: Integers m,n Yes/No question: Is m a divisor of n?
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3 Graph Theory Problems These are problems where we investigate properties of graphs Connected Input: Graph G Yes/No Question: Is G a connected graph? Subgraph • Input: Graphs G 1 and G 2 • Yes/No question: Is G 1 a subgraph of G 2 ?
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4 Program Behavior Problems These are problems where we investigate properties of programs and how they behave Give an example problem with one input program P Give an example problem with two input programs P 1 and P 2
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5 Program Representation Program variables Abstractly, we define the type “program” graph G, program P More concretely, we define type program to be
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Unformatted text preview: a string over the program alphabet Σ P = {a, …, z, A, …, Z, 0, …, 9, punctuation, white space} • Note, many strings over Σ P are not legal programs • We consider them to be programs that always crash • Possible declaration of main procedure – bool main(program P) 6 Program correctness • How do we determine whether or not a program P we have written is correct? • What are some weaknesses of this approach? • What might be a better approach? 7 Testing versus Analyzing Program P Test Inputs x 1 x 2 x 3 ... Outputs P(x 1 ) P(x 2 ) P(x 3 ) ... Analyzer Program P Analysis of Program P 8 2 Program Behavior Problems * • Correctness – Input • Program P – Yes/No Question • Does P correctly solve the primality problem? • Functional Equivalence – Input • Programs P 1 , P 2 – Yes/No Question • Is program P 1 functionally equivalent to program P 2...
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This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.

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Module06 - a string over the program alphabet Σ P ={a …...

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