New inference rules for Max-SAT

  • Authors:

  • Chu Min Li;Felip Manyà;Jordi Planes

  • Affiliations:

  • LaRIA, Université de Picardie Jules Verne, Amiens Cedex 01, France;IIIA, Artificial Intelligence Research Institute, CSIC, Spanish National Research Council, Bellaterra, Spain;Computer Science Department, Universitat de Lleida, Lleida, Spain

  • Venue:
  • Journal of Artificial Intelligence Research
  • Year:
  • 2007

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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 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. With the aim of finding 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 provide empirical evidence that MaxSatz is very competitive, at least, on random Max-2SAT, random Max-3SAT, Max-Cut, and Graph 3-coloring instances, as well as on the benchmarks from the Max-SAT Evaluation 2006.