Does This Set of Clauses Overlap with at Least One MUS?

  • Éric Grégoire
  • Bertrand Mazure
  • Cédric Piette
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5663)


This paper is concerned with the problem of checking whether a given subset Γ of an unsatisfiable Boolean CNF formula Σ takes part in the basic causes of the inconsistency of Σ. More precisely, an original approach is introduced to check whether Γ overlaps with at least one minimally unsatisfiable subset (MUS) of Σ. 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 Σ 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.


Conjunctive Normal Form Local Inconsistency Conjunctive Formula Critical Clause Promising Cluster 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Éric Grégoire
    • 1
  • Bertrand Mazure
    • 1
  • Cédric Piette
    • 1
  1. 1.Université Lille-Nord de France, Artois, CRIL-CNRS UMR 8188Lens CedexFrance

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