A Recursive Algorithm for Projected Model Counting

Abstract

We present a recursive algorithm for projected model counting, i.e., the problem consisting in determining the number of models k∃X.Σk of a propositional formula Σ after eliminating from it a given set X of variables. Based on a ”standard” model counter, our algorithm projMC takes advantage of a disjunctive decomposition scheme of ∃X.Σ for computing k∃X.Σk. It also looks for disjoint components in its input for improving the computation. Our experiments show that in many cases projMC is significantly more efficient than the previous algorithms for projected model counting from the literature.