Searching for Autarkies to Trim Unsatisfiable Clause Sets

An autarky is a partial assignment to the variables of a Boolean CNF formula that satisfies every clause containing an assigned variable. For an unsatisfiable formula, an autarky provides information about those clauses that are essentially independent from the infeasibility; clauses satisfied by an autarky are not contained in any minimal unsatisfiable subset (MUS) or minimal correction subset (MCS) of clauses. This suggests a preprocessing step of detecting autarkies and trimming such independent clauses from an instance prior to running an algorithm for finding MUSes or MCSes. With little existing work on algorithms for finding autarkies or experimental evaluations thereof, there is room for further research in this area. Here, we present a novel algorithm that searches for autarkies directly using a standard satisfiability solver. We investigate the autarkies of several industrial benchmark suites, and experimental results show that our algorithm compares favorably to an existing approach for discovering autarkies. Finally, we explore the potential of trimming autarkies in MCSor MUS-extraction flows.