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- W2950782526 abstract "We give a complexity dichotomy for the problem of computing the partition function of a weighted Boolean constraint satisfaction problem. Such a problem is parameterized by a set of rational-valued functions, which generalize constraints. Each function assigns a weight to every assignment to a set of Boolean variables. Our dichotomy extends previous work in which the weight functions were restricted to being non-negative. We represent a weight function as a of the form (-1)^s g, where the polynomial s determines the sign of the weight and the non-negative function g determines its magnitude. We show that the problem of computing the partition function (the sum of the weights of all possible variable assignments) is in polynomial time if either every weight function can be defined by a pure affine magnitude with a quadratic sign polynomial or every function can be defined by a magnitude of product type with a linear sign polynomial. In all other cases, computing the partition function is FP^#P-complete." @default.
- W2950782526 created "2019-06-27" @default.
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- W2950782526 date "2008-12-22" @default.
- W2950782526 modified "2023-10-18" @default.
- W2950782526 title "The Complexity of Weighted Boolean #CSP with Mixed Signs" @default.
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