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

  • Gennady Davydov
  • Inna Davydova
  • Hans Kleine Büning
Article

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.

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Gennady Davydov
    • 1
  • Inna Davydova
    • 1
  • Hans Kleine Büning
    • 2
  1. 1.Faculty of Math.–Mech.Institute of Transport Problems, Russian Academy of SciencesSt. PetersburgRussia
  2. 2.Department of Mathematics and Computer ScienceUniversity of PaderbornPaderbornGermany

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