Model counting using the inclusion-exclusion principle

Abstract

The inclusion-exclusion principle is a well-known mathematical principle used to count the number of elements in the union of a collection of sets in terms of intersections of sub-collections.We present an algorithm for counting the number of solutions of a given k-SAT formula using the inclusion-exclusion principle. The key contribution of our work consists of a novel subsumption pruning technique. Subsumption pruning exploits the alternating structure of the terms involved in the inclusion-exclusion principle to discover term cancellations that can account for the individual contributions of a large number of terms in a single step. © 2011 Springer-Verlag.