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**Unformatted text preview: **Computer Science E-207 A Reduction 1. NP-completeness. A language L is said to be NP-complete iff L is in NP ; and L is NP-hard (i.e. every language in NP is reducible to L in polynomial time). To show L is in NP : Show that L has succinct certificates that can be nondeterministically guessed; and Give a polynomial time algorithm that checks the certificates. To show L is NP-hard: Choose a known NP-complete language L to reduce from. Reduce L to L . Show that the reduction can be done in polynomial time. What are some known NP-complete languages? Sat, 3-Sat, Integer Linear Programming, Vertex Cover, Clique, Independent Set . What should the reduction look like? We begin with a problem X and a known NP-complete problem X . We want to show that if we had some deterministic polynomial time algorithm for solving X , we could use it to solve X in deterministic polynomial time. To do this, we have to be able to transform every instance of the problem X into an instance of the problem...

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