New Inference Rules for Max-SAT

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 formula is not equivalent to solving it for the original formula. In this paper, we define a number of original inference rules that, besides being applied efficiently, transform Max-SAT instances into equivalent Max-SAT instances which are easier to solve. The soundness of the rules, that can be seen as refinements of unit resolution adapted to Max-SAT, are proved in a novel and simple way via an integer programming transformation. Aiming to find out how powerful the inference rules are in practice, we have developed a new Max-SAT solver, called MaxSatz, which incorporates those rules, and performed an experimental investigation. The results obtained provide empirical evidence that MaxSatz is very competitive and greatly outperforms the best stateof-the-art Max-SAT solvers on random Max-2SAT, random Max-3SAT, Max-Cut, and Graph 3-coloring instances, as well as benchmarks submitted to the Max-SAT Evaluation 2006.