Counting Minimal Unsatisfiable Subsets

Abstract Given an unsatisfiable Boolean formula F in CNF, subset of clauses U is called Minimal Unsatisfiable Subset (MUS) if every proper satisfiable. Since MUSes serve as explanations for the unsatisfiability , find applications a wide variety domains. The availability efficient SAT solvers has aided development scalable techniques finding and enumerating past two decades. Building on recent developments design model counting SAT, Bendík Meel initiated study MUS techniques. They succeeded designing first approximate counter, $$\mathsf {AMUSIC}$$ AMUSIC that does not rely exhaustive enumeration. however, suffers from shortcomings: lack exact estimates limited scalability due to its reliance 3-QBF solvers. In this work, we address shortcomings by {CountMUST}$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">CountMUST circumvents need reducing problem projected counting. While #NP-hard, few years have witnessed counters. An extensive empirical evaluation demonstrates successfully returns count 1500 instances while enumeration-based could only handle up 833 instances.