Complexities of Renaming for Formulas in MAX(1) and MARG(1)

Abstract

A renaming is a function mapping propositional variable to itself or its complement, a variable renaming is a permutation over the set of propositional variables of a formula, and a literal renaming is a combination of a renaming and a variable renaming. Renaming for CNF formulas may help to improve DPLL algorithm. This paper investigates the complexity of decision problem: for propositional CNF formulas H and F, does there exist a variable (or literal) renaming such that (H)=F? Both MAX(1) and MARG(1) are subclasses of the minimal unsatisfiable formulas, and formulas in these subclasses can be represented by trees. The decision problem of isomorphism for trees is solvable in linear time. Formulas in the MAX(1) and MARG(1), it is shown that the literal renaming problems are solvable in linear time, and the variable renaming problems are solvable in quadratic time.