November 29

# November 29 - CSCI 2670 Introduction to Theory of Computing...

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CSCI 2670 Introduction to Theory of Computing November 29, 2005

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November 29, 2005 Agenda •Today – More on the class NP
November 29, 2005 Announcement

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November 29, 2005 The class NP Definition: A verifier for a language A is an algorithm V, where A={w|V accepts <w,c> for some string c} The string c is called a certificate of membership in A. Definition: NP is the class of languages that have polynomial-time verifiers.
November 29, 2005 Who wants \$1,000,000? • In May, 2000, the Clay Mathematics Institute named seven open problems in mathematics the Millennium Problems – Anyone who solves any of these problems will receive \$1,000,000 – Proving whether or not P equals NP is one of these problems

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November 29, 2005 What we know NP Pc o
November 29, 2005 What we don’t know NP Pc o N

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November 29, 2005 Solving NP problems • The best-known methods for solving problems in NP that are not known to be in P take exponential time – Brute force search
November 29, 2005 NP-completeness A problem C is NP-complete if finding a polynomial-time solution for C would imply P=NP Definition: A language B is NP-complete if it satisfies two conditions: 1. B is in NP, and 2. Every A in NP is polynomial time reducible to B

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November 29, 2005 An NP-complete problem • A formula is Boolean if each of its variables can be assigned the values
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November 29 - CSCI 2670 Introduction to Theory of Computing...

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