An Isomorphism-Invariant Distance Function on Propositional Formulas in CNF

Abstract

We define a distance function on propositional formulas in CNF as a measure of non-isomorphism of formulas: the larger the distance between two formulas is, the further they are from being isomorphic. This distance induces a metric on isomorphism classes of formulas. We show how this distance can be used for SAT solving, namely for per-instance algorithm selection where there is a “portfolio” of SAT solvers and there is a “meta-solver” that chooses a solver from the portfolio for a given input formula.