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

The maximum satisfiability problem (MAX-SAT) is stated as follows: Given Boolean formula in CNF, find a truth assignment that satisfies the maximum possible number of its clauses. MAX-SAT is MAX-SNP-complete and received much attention recently. One of the challenges posed by Alber, Gramm

Abstract. Exact Max-SAT solvers, compared with SAT solvers, apply little inference at each node of the proof tree. Commonly used SAT inference rules like unit propagation produce a simplified formula that preserves satisfiability but, unfortunately, solving the Max-SAT problem for the simplified

MAX SAT (the maximum satisfiability problem) is stated as follows: given a set of clauses with weights, find a truth assignment that maximizes the sum of the weights of the satisfied clauses. In this paper, we consider approximation algorithms for MAX SAT proposed by Goemans and Williamson

In this paper we present a 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. The key idea is to add an additional variable to each soft clause and to introduce

Abstract. Solving over-constrained problems with Max-SAT solvers typically consists of finding an assignment that satisfies all the hard constraints and the maximum number of soft constraints. Despite the relevance of clause learning in SAT for solving structured instances, this technology has

Abstract. In this paper we introduce MINIMAXSAT, a new Max-SAT solver that incorporates the best SAT and Max-SAT techniques. It can handle hard clauses (clauses of mandatory satisfaction as in SAT), soft clauses (clauses whose falsification is penalized by a cost as in Max-SAT) as well as pseudo

Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses of a given 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

We describe the organization and report on the results of the First and Second Max-SAT Evaluations, which were organized as affiliated events of the 2006 and 2007 editions of the International Conference on Theory and Applications of Satisfiability Testing (SAT-2006 and SAT-2007), discuss

important variation, the Partial MAX-SAT problem. Unlike SAT, Partial MAX-SAT has certain constraints (clauses) that are marked as relaxable and the rest are hard, i.e. non-relaxable. The objective is to find a variable assignment that satisfies all non-relaxable clauses together with the maximum number