A Logical Approach to Efficient Max-SAT solving

INRA Toulouse, France Abstract Weighted Max-SA T is the optimization version of SA T and many important problems can be naturally encoded as such. Solving weighted Max-SA T is an important problem from both a theoretical and a practical point of view. In recent ye ars, there has been considerable interest in finding efficient solving techniques. Most of thi s work focus on the computation of good quality lower bounds to be used within a branch and bou nd DPLL-like algorithm. Most often, these lower bounds are described in a procedural way. Because of that, it is difficult to realize the logic that is behind. In this paper we introduce an original framework for Max-SA T that stresses the parallelism with classical SA T. Then, we extend the two basic SA T s olving techniques: search and inference. We show that many algorithmic tricks used in state-of-the-art Max-SA T solvers are easily expressable in logic terms with our framework in a unified manner. Besides, we introduce an original search algorithm that per forms a restricted amount of weighted resolution at each visited node. We empirically compare our algorithm w ith a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat eva luation ever reported, show that our algorithm is generally orders of magnitude faster t han any competitor. Preprint submitted to Elsevier Science 11 September 2018 1 Introduction Weighted Max-SA T is the optimization version of the SA T prob lem and many important problems can be naturally expressed as such. In recent years, there has been a considerable effort in finding efficient exact algorithms. A common drawback of all these alg orithms is that albeit the close relationship between SA T and Max-SA T, they cannot be easily described with logic terminology. For instance, the contributions of [11,12,13,14] are good quality lower bounds to be incorporated into a depth-first branch and bound procedure. These lower bounds are mostly defined in a procedural way and it is very difficult to see the logic that is behind the execution of the procedure. This is in contrast with SA T algorithms where the solving process can b e easily decomposed into atomic logical steps. In this paper we introduce an original framework for (weight ed) Max-SA T in which the notions of upper and lower bound are incorporated into the problem definition. Under this framework classical SA T is just a particular case of Max-SA T, and the main SA T solving techniques can be naturally extended. In pa rticular, we extend the basic simplification rules (for example, idempotency, absorption, unit clause reduction, etc) and introduce a new one, hardening, that does not make sense in the SA T context.