Clausal Forms in MaxSAT and MinSAT

Abstract

Abstract 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.

Keywords

• Maximum satisfiability problem
• Minimum satisfiability problem
• Clausal forms