Cook - Complexity 1 Our First NP-Complete Problem The Cook-Levin theorem A B C Complexity 2 2 Introduction • Objectives – To present the first

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Unformatted text preview: Complexity 1 Our First NP-Complete Problem The Cook-Levin theorem A B C Complexity 2 2 Introduction • Objectives : – To present the first NP-Complete problem • Overview : – SAT- definition and examples – The Cook-Levin theorem – What next? Complexity 3 SAT • Instance : A Boolean formula. • Problem : To decide if the formula is satisfiable. ) x (x ) x ) x x ((x 2 3 1 3 2 1 ∧ ¬ ∨ ¬ ∧ ¬ ∨ ∨ F T A satisfiable Boolean formula: F T T T An unsatisfiable Boolean formula: 1 1 x x ¬ ∧ Complexity 4 Co-NP To Which Time Complexity Class Does SAT Clearly Belong? NP P SAT Complexity 5 SAT is in NP: Non-Deterministic Algorithm • Guess an assignment to the variables. • Check the assignment. ) x (x ) x ) x x ((x 2 3 1 3 2 1 ∧ ¬ ∨ ¬ ∧ ¬ ∨ ∨ F T F T T T x 1 x 2 x 3 F T T Complexity 6 The Cook-Levin Theorem: SAT is NP- Complete Proof Idea : For any NP machine M and any input string w , we construct a Boolean formula ϕ M,w which is satisfiable iff M accepts w ....
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This note was uploaded on 07/14/2011 for the course COT 5310 taught by Professor Staff during the Spring '08 term at University of Central Florida.

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Cook - Complexity 1 Our First NP-Complete Problem The Cook-Levin theorem A B C Complexity 2 2 Introduction • Objectives – To present the first

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