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Maximum Satisfiability (MaxSat) solving is an active area of research motivated by numerous successful applications to solving NP-hard combinatorial optimization problems. One of the most successful approaches to solving MaxSat instances arising from real world applications is the Implicit Hitting Set (IHS) approach. IHS solvers are complete MaxSat solvers that harness the strengths of both Boolean Satisfiability (SAT) and Integer Linear Programming (IP) solvers by decoupling core-extraction and optimization. While such solvers show state-of-the-art performance on many instances, it is known that there exist MaxSat instances on which IHS solvers need to extract an exponential number of cores before terminating. Motivated by the structure of the simplest of these problematic instances, we propose a technique we call abstract cores that provides a compact representation for a potentially exponential number of regular cores. We demonstrate how to incorporate abstract core reasoning into the IHS algorithm and report on an empirical evaluation demonstrating that including abstract cores into a state-of-the-art IHS solver improves its performance enough to surpass the best performing solvers of the most recent 2019 MaxSat Evaluation.

Abstract Cores in Implicit Hitting Set MaxSat Solving