max-sat - Discrete Structures CS 280 Example application of...

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CS 280 Example application of probability: MAX 3-SAT 1
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MAX 3-SAT Consider a propositional logical formula on N Boolean variables in conjunctive normal form (CNF), i.e., a conjunction (logical AND) of disjunctions (logical OR). Example: The truth assignment with and assigned to True and assigned to False satisfies this formula. Each disjunction is also referred to as a “ clause ”. If each clause contains exactly k variables, the formula is a k-CNF formula . 12 32 3 3 () ( ) ( ) xx x x ¬∨∧∨∧ ¬ 1 x 2 x 3 x
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MAX 3-SAT cont. Problem: MAX-3-SAT Given a 3-CNF formula F , find a truth assignment that satisfies as many clauses as possible. The MAX 3-SAT problem is a so-called NP-hard problem; it is generally believed that no efficient (i.e., polynomial time) algorithm exists for solving such problems. [The $1M Clay Millennium prize, click on P=/=NP 3 ] Note that we have a search space of 2 N truth assignments. Stephen Cook Leonid Levin
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4 So, finding a maximally satisfying assignment is (most likely) computationally very hard.
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max-sat - Discrete Structures CS 280 Example application of...

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