A logical approach to efficient Max-SAT solving

Abstract

Weighted Max-SAT is the optimization version of SAT and many important problems can be naturally encoded as such. Solving weighted Max-SAT is an important problem from both a theoretical and a practical point of view. In recent years, there has been considerable interest in finding efficient solving techniques. Most of this work focus on the computation of good quality lower bounds to be used within a branch and bound 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-SAT that stresses the parallelism with classical SAT. Then, we extend the two basic SAT solving techniques: search and inference. We show that many algorithmic tricks used in state-of-the-art Max-SAT solvers are easily expressable in logic terms with our framework in a unified manner.Besides, we introduce an original search algorithm that performs a restricted amount of weighted resolution at each visited node. We empirically compare our algorithm with a variety of solving alternatives on several benchmarks. Our experiments, which constitute to the best of our knowledge the most comprehensive Max-sat evaluation ever reported, show that our algorithm is generally orders of magnitude faster than any competitor.⋆ This paper includes and extends preliminary work from [1,2]

A Max-SAT Inference-Based Pre-processing for Max-Clique

“…As shown in [16], the De Morgan rule cannot be used in Max-SAT. Instead, the following rule should be repeatedly used until CNF is achieved:…”

“…The following notation and terminology has been borrowed from [16]. In the sequel X is a set of boolean variables taking values over the set {t, f }, which stands for true and false, respectively.…”

“…Following [16], we assume without loss of generality the existence of a known upper bound of the optimal solution ( is a strictly positive natural number). A model is a complete assignment with cost less than .…”

“…We introduce two simplification rules for the Max-Clique problem based on the resolution rule for Max-SAT [16] and we apply them in a preprocessing procedure. The result of the pre-process is an equivalent Max-SAT formula with an explicit lower bound of the optimum.…”

Clone: Solving Weighted Max-SAT in a Reduced Search Space

“…Toolbar utilizes local consistencies to aid bound computations [5,6]. Lazy, MaxSatz, and MiniMaxSat compute bounds using some variations of unit propagation and disjoint component detection [7][8][9][10].…”