MAX(1)和MARG(1)中公式改名的复杂性

改名是一个将变元映射到变元本身或它的补的函数,变元改名是公式变元集合上的一个置换,文字改名是一个改名和一个变元改名的组合.研究CNF公式的改名有助于改进DPLL算法.考虑判定问题"对于给定的CNF公式H和F是否存在一个变元(或文字)改名ψ使得ψ(H)=F?"的计算复杂性.MAX(1)和MARG(1)是极小不可满足公式的两个子类,这两个子类中的公式可以用树表示.树同构的判定问题在线性时间内是可解的.证明了对于MAX(1)和MARG(1)中的公式,文字改名问题在线性时间内可解,变元改名问题在平方次时间内可解.

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

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 ψ such that ψ(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.