Maximum Satisfiability Problem: Computational complexity theory, Propositional formula, NP-hard, Boolean satisfiability problem, NP-complete, APX - Tapa blanda

Sinopsis

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In computational complexity theory, the Maximum Satisfiability problem, or MAX-SAT, is the problem of determining the maximum number of clauses, of a given Boolean formula, that can be satisfied by some assignment. The MAX-SAT problem is NP-hard, since its solution easily leads to the solution of the boolean satisfiability problem, which is NP-complete. It is also APX-complete, and thus does not admit a PTAS unless P = NP. MAX-SAT is one of the optimization extensions of the boolean satisfiability problem, which is the problem of determining if the variables of a given Boolean formula can be assigned in such a way as to make the formula evaluate to TRUE. If the clauses are restricted to have at most 2 literals, as in 2-satisfiability, we get the MAX-2SAT problem. If they are restricted to at most 3 literals per clause, as in 3-satisfiability, we get the MAX-3SAT problem.

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