At each node of the search tree, Branch and Bound solvers for Max-SAT compute the lower bound (LB) by estimating the number of disjoint inconsistent subsets (IS) of the formula. IS are detected thanks to unit propagation (UP) then transformed by max-resolution to ensure that they are counted only once. However, it has been observed experimentally that the max-resolution transformations impact the capability of UP to detect further IS. Consequently, few transformations are learned and the LB computation is redundant. In this paper, we study the effect of the transformations on the UP mechanism. We introduce the notion of UP-resiliency of a transformation, which quantifies its impact on UP. It provides, from a theoretical point of view, an explanation to the empirical efficiency of the learning scheme developed in the last ten years. The experimental results we present give evidences of UP-resiliency relevance and insights on the behavior of the learning mechanism.

Core-guided approaches to solving MAXSAT have proved to be effective on industrial problems. These approaches solve a MAXSAT formula by building a sequence of SAT formulas, where in each formula a greater weight of soft clauses can be relaxed. The soft clauses are relaxed via the addition of blocking variables, and the total weight of soft clauses that can be relaxed is limited by placing constraints on the blocking variables. In this work we propose an alternative approach. Our approach also builds a sequence of new SAT formulas. However, these formulas are constructed using MAXSAT resolution, a sound rule of inference for MAXSAT. MAXSAT resolution can in the worst case cause a quadratic blowup in the formula, so we propose a new compressed version of MAXSAT resolution. Using compressed MAXSAT resolution our new core-guided solver improves the state-of-theart, solving significantly more problems than other state-ofthe-art solvers on the industrial benchmarks used in the 2013 MAXSAT Solver Evaluation.

In this paper we introduce MiniMaxSat, a new Max-SAT solver that is built on top of MiniSat+. It incorporates the best current 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-boolean objective functions and constraints. Its main features are: learning and backjumping on hard clauses; resolution-based and substraction-based lower bounding; and lazy propagation with the two-watched literal scheme. Our empirical evaluation comparing a wide set of solving alternatives on a broad set of optimization benchmarks indicates that the performance of MiniMaxSat is usually close to the best specialized alternative and, in some cases, even better.