Does this set of clauses overlap with at least one MUS?

Abstract

This paper is concerned with the problem of checking whether a given subset F of an unsatisfiable Boolean CNF formula ∑ takes part in the basic causes of the inconsistency of ∑. More precisely, an original approach is introduced to check whether F overlaps with at least one minimally unsatisfiable subset (MUS) of ∑. In the positive case, it intends to compute and deliver one such MUS. The approach re-expresses the problem within an evolving coarser-grained framework where clusters of clauses of ∑ are formed and examined according to their levels of mutual conflicts when they are interpreted as basic interacting entities. It then progressively refines the framework and the solution by splitting most promising clusters and pruning the useless ones until either some maximal preset computational resources are exhausted, or a final solution is discovered. The viability and the usefulness of the approach are illustrated through benchmarks experimentations. © 2009 Springer Berlin Heidelberg.