Accelerating MUS enumeration by inconsistency graph partitioning

Abstract

The problem of finding minimal unsatisfiable subsets (MUSes) has been studied frequently because of itstheoretical importance and wide range of applications in domains such as electronic design automation,software, and integrated circuit verification. In this paper, a method for accelerating theenumeration of MUSes based on inconsistency graph partitioning is proposed. First, an inconsistency graphof a set of clauses is constructed by extracting the inconsistencyrelations between literals of different clauses. In this paper, we show that by partitioning the inconsistency graphinto small connected components through a vertex cut, the enumeration of MUSes in different componentsbecomes independent and it is possible to compute them separately. Moreover, the MUSes of the original clause setcan be constructed by merging the unit clauses in the MUSes of these connected components back into the clauses inthe vertex cut. Experiments show that by integrating the acceleration method into the MARCO MUSes enumerator,there is a 2–3 times improvement in the average runtime of solved instances for randomly generatedbenchmarks. By integrating the acceleration method into itself as an MUS enumerator, there isanother 3–4 times improvement when compared with the accelerated MARCO.