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

Authors:
Gennady Davydov;Inna Davydova;Hans Kleine Büning
Affiliations:
Faculty of Math.–Mech., Institute of Transport Problems, Russian Academy of Sciences, P.O. Box 20, 199053, St. Petersburg, Russia E-mail: inna@davy.usr.pu.ru;Faculty of Math.–Mech., St. Petersburg State University, P.O. Box 20, 199053, St. Petersburg, Russia E-mail: inna@davy.usr.pu.ru;Department of Mathematics and Computer Science, University of Paderborn, D‐33095 Paderborn, Germany E-mail: kbcsl@uni‐paderborn.de
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
1998

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Abstract

We consider the minimal unsatisfiability problem for propositional formulas over n variables with n+k clauses for fixed k. 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+1 clauses in terms of a certain form of matrices.