Abstract
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.
Research partially funded by French ANR UNLOC project: ANR-08-BLAN-0289-03, National Natural Science Foundation of China (NSFC) grant No. 61070235, the Generalitat de Catalunya under grant AGAUR 2009-SGR-1434, the Ministerio de Economía y Competividad research projects AT CONSOLIDER CSD2007-0022, INGENIO 2010, ARINF TIN2009-14704-C03-01, TASSAT TIN2010-20967-C04-01/03, and Newmatica INNPACTO IPT-2011-1496-310000 (funded by the Ministerio de Ciencia y Tecnología until 2011).
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Zhu, Z., Li, CM., Manyà, F., Argelich, J. (2012). A New Encoding from MinSAT into MaxSAT. In: Milano, M. (eds) Principles and Practice of Constraint Programming. CP 2012. Lecture Notes in Computer Science, vol 7514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33558-7_34
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DOI: https://doi.org/10.1007/978-3-642-33558-7_34
Publisher Name: Springer, Berlin, Heidelberg
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