Local-search Extraction of MUSes

SAT is probably one of the most-studied constraint satisfaction problems. In this paper, a new hybrid technique based on local search is introduced in order to approximate and extract minimally unsatisfiable subformulas (in short, MUSes) of unsatisfiable SAT instances. It is based on an original counting heuristic grafted to a local search algorithm, which explores the neighborhood of the current interpretation in an original manner, making use of a critical clause concept. Intuitively, a critical clause is a falsified clause that becomes true thanks to a local search flip only when some other clauses become false at the same time. In the paper, the critical clause concept is investigated. It is shown to be the cornerstone of the efficiency of our approach, which outperforms competing ones to compute MUSes, inconsistent covers and sets of MUSes, most of the time.