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Resolution for Max-SAT

AuthorsBonet, M. Luisa; Levy, Jordi ; Manyà, Felip
Weighted Max-SAT
Issue Date2007
CitationArtificial Intelligence 171: 606- 618 (2007)
AbstractMax-SAT is the problem of finding an assignment minimizing the number of unsatisfied clauses in a 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. We also define a weighted Max-SAT resolution-like rule, and show how to adapt the soundness and completeness proofs of the Max-SAT rule to the weighted Max-SAT rule. Finally, we give several particular Max-SAT problems that require an exponential number of steps of our Max-SAT rule to obtain the minimal number of unsatisfied clauses of the combinatorial principle. These results are based on the corresponding resolution lower bounds for those particular problems. © 2007 Elsevier B.V. All rights reserved.
Identifiersdoi: 10.1016/j.artint.2007.03.001
issn: 0004-3702
Appears in Collections:(IIIA) Artículos
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