The Complexity of Homomorphisms and Renamings for Minimal Unsatisfiable Formulas

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 ? such that ?(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.