63 Slides--Reductions from NPC

# 63 Slides--Reductions from NPC - CS103 HO#63...

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Unformatted text preview: CS103 HO#63 Slides--Reductions from NPC June 2, 2010 1 CS103 Mathematical Foundations of Computing 6/2/10 FINAL EXAM: Friday, June 4, 12:15 – 3:15 Room Assignments Last Name A – L: Hewlett 201 Last Name M – Z: 420-041 B NP-Completeness P NP NPC Theorem 7.31 : If A P B and B P, then A P. Definition 7.34 : A language B is NP-complete if B NP and every A NP is polynomial time reducible to B. Theorem 7.35 : If B is NP-complete and B P, then P = NP. Theorem 7.36 : If B is NP-complete and B P C for C NP, then C NPC. P P P P C P Decidable(B) Decidable(A) ¬ Decidable(A) ¬ Decidable(B) Map the problem to B Problem for A Decider for B Decider for A Problem for B Decision for A w B ↔ f(w) C B NPC C NP f poly time C NPC Problem for B NPC Problem for C f f Map the problem to C NP in poly time SAT P NP NPC Theorem 7.37 : SAT is NP-complete. (The Cook-Levin Theorem) Theorem 7.37 : SAT is NP-complete. (The Cook-Levin Theorem) Corollary 7.42 : 3SAT is NP-complete. 3SAT = { | is satisfiable and is a 3cnf-formula } Conjunctive Normal Form : a conjunction of disjunctions of literals (x 1 x 2 ) (x 3 x 4 x 5 x 6 ) (x 3 x 5 x 6 ) 3-cnf : all clauses have three literals (x 1 x 2 x 3 ) (x 3 x 4 x 5 ) (x 2 x 5 x 6 ) (x 1 x 4 x 5 ) Theorem 7.37 : SAT is NP-complete. (The Cook-Levin Theorem) Corollary 7.42 : 3SAT is NP-complete....
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63 Slides--Reductions from NPC - CS103 HO#63...

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