Abstract. In this paper, a new pre-processing step is proposed in the resolution of SAT instances, that recovers and exploits structural knowledge that is hidden in the CNF. It delivers an hybrid formula made of clauses together with a set of equations of the form y = f (x1, . . . , xn) where f is a standard connective operator among (∨, ∧, ⇔) and where y and xi are boolean variables of the initial SAT instance. This set of equations is then exploited to eliminate clauses and variables, while preserving satisfiability. These extraction and simplification techniques allowed us to implement a new SAT solver that proves to be the most efficient current one w.r.t. several important classes of instances.
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 f alse 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.