Re-using Auxiliary Variables for MaxSAT Preprocessing

Solvers for the maximum satisfiability (MaxSAT) problem -- a well-known optimization variant of Boolean satisfiability (SAT) -- are finding an increasing number of applications. Preprocessing has proven an integral part of the SAT-based approach to efficiently solving various types of real-world problem instances. It was recently shown that SAT preprocessing for MaxSAT becomes more effective by re-using the auxiliary variables introduced in the preprocessing phase directly in the SAT solver within a core-based hybrid MaxSAT solver. We take this idea of re-using auxiliary variables further by identifying them among variables already present in the input MaxSAT instance. Such variables can be re-used already in the preprocessing step, avoiding the introduction of multiple layers of new auxiliary variables in the process. Empirical results show that by detecting auxiliary variables in the input MaxSAT instances can lead to modest additional runtime improvements when applied before preprocessing. Furthermore, we show that by re-using auxiliary variables not only within preprocessing but also as assumptions within the SAT solver of the MaxHS MaxSAT algorithm can alone lead to performance improvements similar to those observed by applying SAT-based preprocessing.