Polynomial time algorithms for computing a representation for minimal unsatisfiable formulas with fixed deficiency

Authors:
Hans Kleine Büning;Xishun Zhao
Affiliations:
Department of Computer Science, Universitait Paderborn, 33095 Paderborn, Germany;Institute of Logic and Cognition, Zhongshan University, 510275 Guangzhou, People's Republic of China
Venue:
Information Processing Letters
Year:
2002

Citing 6
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Abstract

We say a propositional formula F in conjunctive normal form is represented by a formula H and a homomorphism φ, if φ(H) = F. A homomorphism is a mapping consisting of a renaming and an identification of literals. The deficiency of a formula is the difference between the number of clauses and the number of variables. We show that for fixed k ≥ 1 and t ≥ 1 each minimal unsatisfiable formula with deficiency k can be represented by a formula H with deficiency t and a homomorphism and such a representation can be computed in polynomial time.