A New Encoding from MinSAT into MaxSAT

MinSAT is the problem of finding a truth assignment that minimizes the number of satisfied clauses in a CNF formula. When we distinguish between hard and soft clauses, and soft clauses have an associated weight, then the problem, called Weighted Partial MinSAT, consists in finding a truth assignment that satisfies all the hard clauses and minimizes the sum of weights of satisfied soft clauses. In this paper we define a novel encoding from Weighted Partial MinSAT into Weighted Partial MaxSAT, which is also valid for encoding Weighted Partial MaxSAT into Weighted Partial MinSAT. Moreover, we report on an empirical investigation that shows that our encoding significantly outperforms existing encodings on weighted and unweighted Min2SAT and Min3SAT instances.

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