Clausal Forms in MaxSAT and MinSAT

• Published in: International journal of computational intelligence systems Vol. 15; pp. 1 - 12
• Main Authors: Li, Chu Min, Manyà, Felip, Soler, Joan Ramon, Vidal, Amanda
• Format: Journal Article
• Language: English
• Published: Atlantis Press 11-11-2022
• Subjects: Computer Science
• ISSN: 1875-6891; 1875-6883
• DOI: 10.1007/s44196-022-00143-z

We tackle the problem of reducing non-clausal MaxSAT and MinSAT to clausal MaxSAT and MinSAT. Our motivation is twofold: (i) the clausal form transformations used in SAT are unsound for MaxSAT and MinSAT, because they do not preserve the minimum or maximum number of unsatisfied clauses, and (ii) the state-of-the-art MaxSAT and MinSAT solvers require as input a multiset of clauses. The main contribution of this paper is the definition of three different cost-preserving transformations. Two transformations extend the usual equivalence preserving transformation used in SAT to MaxSAT and MinSAT. The third one extends the well-known Tseitin transformation. Furthermore, we report on an empirical comparison of the performance of the proposed transformations when solved with a state-of-the-art MaxSAT solver.