The Complexity of Homomorphisms and Renamings for Minimal Unsatisfiable Formulas

Authors:
Hans Kleine Büning;Daoyun Xu
Affiliations:
Department of Computer Science, Universität Paderborn, 33095 Paderborn, Germany E-mail: kbcsl@upb.de;Department of Computer Science, Guizhou University, 550025 Guiyang, P.R. China E-mail: daoyun.gzu@263.net
Venue:
Annals of Mathematics and Artificial Intelligence
Year:
2005

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Abstract

We investigate the complexity of deciding whether for minimal unsatisfiable formulas F and H there exists a variable renaming, a literal renaming or a homomorphism φ such that φ(F)=H. A variable renaming is a permutation of variables. A literal renaming is a permutation of variables which additionally replaces some of the variables by its complements. A homomorphism can be considered as a literal renaming which can map different literals to one literal.