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Resolution for Max-SAT
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DOI：10.1016/j.artint.2007.03.001.png)
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Abstract
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Max-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. (c) 2007 Elsevier B.V. All rights reserved.
Keywords:
satisfiability
resolution
completeness
saturation
Max-SAT
weighted Max-SAT
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