63 Slides--Reductions from NPC

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

Page1 / 5

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online