A New Exact Solver for (Weighted) Max#SAT

Authors Gilles Audemard , Jean-Marie Lagniez , Marie Miceli

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Gilles Audemard
  • CRIL, Univ. Artois & CNRS, Lens, France
Jean-Marie Lagniez
  • CRIL, Univ Artois & CNRS, Lens, France
Marie Miceli
  • CRIL, Univ Artois & CNRS, Lens, France

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Gilles Audemard, Jean-Marie Lagniez, and Marie Miceli. A New Exact Solver for (Weighted) Max#SAT. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 28:1-28:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We present and evaluate d4Max, an exact approach for solving the Weighted Max#SAT problem. The Max#SAT problem extends the model counting problem (#SAT) by considering a tripartition of the variables {X, Y, Z}, and consists in maximizing over X the number of assignments to Y that can be extended to a solution with some assignment to Z. The Weighted Max#SAT problem is an extension of the Max#SAT problem with weights associated on each interpretation. We test and compare our approach with other state-of-the-art solvers on the challenging task in probabilistic inference of finding the marginal maximum a posteriori probability (MMAP) of a given subset of the variables in a Bayesian network and on exist-random quantified SSAT benchmarks. The results clearly show the overall superiority of d4Max in term of speed and number of instances solved. Moreover, we experimentally show that, in general, d4Max is able to quickly spot a solution that is close to optimal, thereby opening the door to an efficient anytime approach.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Search methodologies
  • Software and its engineering → Software notations and tools
  • Max#SAT
  • EMaj-SAT
  • Weighted Projected Model Counting
  • SSAT


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