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Recently, Fu and Malik described an unweighted Partial MaxSAT solver based on successive calls to a SAT solver. At the kth iteration the SAT solver tries to certify that there exist an assignment that satisfies all but k clauses. Later Marques-Silva and Planes implemented and extended these ideas. In this paper we present and implement two Partial MaxSAT(More)
Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses in a CNF formula. We propose a resolution-like calculus for Max-SAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for Max-SAT and a time upper(More)
The search of a precise measure of what hardness of SAT instances means for state-of-the-art solvers is a relevant research question. Among others, the space complexity of treelike resolution (also called hardness), the minimal size of strong backdoors and of cycle-cutsets, and the treewidth can be used for this purpose. We propose the use of the tree-like(More)
We propose an extension of rewriting techniques to derive inclusion relations a ⊆ b between terms built from monotonic operators. Instead of using only a rewriting relation ⊆ −→ and rewriting a to b, we use another rewriting relation ⊇ −→ as well and seek a common expression c such that a ⊆ −→ ∗ c and b ⊇ −→ ∗ c. Each component of the bi-rewriting system 〈(More)
We present a new class of second-order unification problems, which we have called linear. We deal with completely general second-order typed unification problems, but we restrict the set of unifiers under consideration: they instantiate free variables by linear terms, i.e. terms where any λ-abstractions bind one and only one occurrence of a bound variable.(More)
In the last few years, there has been a significant effort in designing and developing efficient Weighted MaxSAT solvers. We study in detail the WPM1 algorithm identifying some weaknesses and proposing solutions to mitigate them. Basically, WPM1 is based on iteratively calling a SAT solver and adding blocking variables and cardinality constraints to relax(More)