Annals of Mathematics and Artificial Intelligence

, Volume 23, Issue 3, pp 229–245

An efficient algorithm for the minimal unsatisfiability problem for a subclass of CNF

Authors

  • Gennady Davydov
    • Faculty of Math.–Mech.Institute of Transport Problems, Russian Academy of Sciences
  • Inna Davydova
    • Faculty of Math.–Mech.Institute of Transport Problems, Russian Academy of Sciences
  • Hans Kleine Büning
    • Department of Mathematics and Computer ScienceUniversity of Paderborn
Article

DOI: 10.1023/A:1018924526592

Cite this article as:
Davydov, G., Davydova, I. & Büning, H.K. Annals of Mathematics and Artificial Intelligence (1998) 23: 229. doi:10.1023/A:1018924526592

Abstract

We consider the minimal unsatisfiability problem for propositional formulas over n variables with n+k clauses for fixedk. We will show that in case of at most n clauses no formula is minimal unsatisfiable. For n+1 clauses the minimal unsatisfiability problem is solvable in quadratic time. Further, we present a characterization of minimal unsatisfiable formulas with n+1clauses in terms of a certain form of matrices.

Copyright information

© Kluwer Academic Publishers 1998