A complete calculus for Max-SAT

Authors:
María Luisa Bonet;Jordi Levy;Felip Manyà
Affiliations:
Dept. Llenguatges i Sistemes Informàtics (LSI), Universitat Politècnica de Catalunya (UPC), Barcelona, Spain;Artificial Intelligence Research Institute (IIIA), Spanish Scientific Research Council (CSIC), Bellaterra, Spain;Artificial Intelligence Research Institute (IIIA), Spanish Scientific Research Council (CSIC), Bellaterra, Spain
Venue:
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Year:
2006

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Abstract

Max-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses of a given CNF formula. We propose a resolution-like calculus for Max-SAT and prove its soundness and completeness. We also prove the completeness of some refinements of this calculus. From the completeness proof we derive an exact algorithm for Max-SAT and a time upper bound.