Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference

Authors:
Herbert Fleischner;Oliver Kullmann;Stefan Szeider
Affiliations:
Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria;Computer Science Department, University of Wales Swansea, Swansea SA2 8PP, United Kingdom;Institute of Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria
Venue:
Theoretical Computer Science
Year:
2002

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Abstract

A formula (in conjunctive normal form) is said to be minimal unsatisfiable if it is unsatisfiable and deleting any clause makes it satisfiable. The deficiency of a formula is the difference of the number of clauses and the number of variables. It is known that every minimal unsatisfiable formula has positive deficiency. Until recently, polynomial-time algorithms were known to recognize minimal unsatisfiable formulas with deficiency 1 and 2. We state an algorithm which recognizes minimal unsatisfiable formulas with any fixed deficiency in polynomial time.