Smallest MUS extraction with minimal hitting set dualization

Abstract

Minimal explanations of infeasibility are of great interest in many domains. In propositional logic, these are referred to as Minimal Unsatisfiable Subsets (MUSes). An unsatisfiable formula can have multiple MUSes, some of which provide more insights than others. Different criteria can be considered in order to identify a good minimal explanation. Among these, the size of an MUS is arguably one of the most intuitive. Moreover, computing the smallest MUS (SMUS) finds several practical applications that include validating the quality of the MUSes computed by MUS extractors and finding equivalent subformulae of smallest size, among others. This paper develops a novel algorithm for computing a smallest MUS, and we show that it outperforms all the previous alternatives pushing the state of the art in SMUS solving. Although described in the context of propositional logic, the presented technique can also be applied to other constraint systems.