NPComplete-handouts-2-2

NPComplete-handouts-2-2 - NP-Completeness (Theorems and...

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Unformatted text preview: NP-Completeness (Theorems and Thoughts)4/24/2006 2:47 PM1NP-Completeness1NP-Completeness (Theorems and Thoughts)x1x3x2x1x4x3x2x4111213212223313233NP-Completeness2TheoremA language L can be deterministically verified in polynomial time if and only if L can be nondeterministically accepted in polynomial timePart 1: If L can be nondeterministically accepted in polynomial time then L can be deterministically verified in polynomial timePart 2: If L can be deterministically verified in polynomial time then L can be nondeterministically accepted in polynomial time NP-Completeness (Theorems and Thoughts)4/24/2006 2:47 PM2NP-Completeness3Equivalence of the Two Definitions (Part 1)Suppose A is a non-deterministic algorithmLet y be a certificate consisting of all the outcomes of the choose steps that A usesWe can create a verification algorithm, B, that uses y instead of the choose steps of AIf A accepts x, then the certificate y allows us to verify this ultimately, using B If A runs in polynomial-time, so does BAAxChooseyiyesNP-Completeness4Equivalence of the Two Definitions (Part 1)(Part 1) Suppose A is a non-deterministic algorithmLet y be a certificate consisting of all the outcomes of the choose steps that A usesWe can create a verification algorithm, B, that uses y instead of the choose steps of AIf A accepts x, then the certificate y allows us to verify...
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This note was uploaded on 09/10/2009 for the course CS 401 taught by Professor Cs401 during the Spring '08 term at Illinois Tech.

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NPComplete-handouts-2-2 - NP-Completeness (Theorems and...

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