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Maximum satisfiability problem
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Maximum satisfiability problem : ウィキペディア英語版
Maximum satisfiability problem
In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula. It is a generalization of the Boolean satisfiability problem, which asks whether there exists a truth assignment that makes all clauses true.
==Example==
The conjunctive normal form formula
: (x_0\lor x_1)\land(x_0\lor\lnot x_1)\land(\lnot x_0\lor x_1)\land(\lnot x_0\lor\lnot x_1)
is not satisfiable: no matter which truth values are assigned to its two variables, at least one of its four clauses will be false.
However, it is possible to assign truth values in such a way as to make three out of four clauses true; indeed, every truth assignment will do this.
Therefore, if this formula is given as an instance of the MAX-SAT problem, the solution to the problem is the number three.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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