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
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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.
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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 P coNP
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November 29, 2005 What we don’t know NP P coNP Are there any problems here?
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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
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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
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This note was uploaded on 02/07/2011 for the course CS 501 taught by Professor Sm during the Spring '11 term at Indiana.

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

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