Model counting of monotone CNF formulas with Spectra

Model-counting is the #P problem of counting the number of satisfying solutions of a given propositional formula. Here we focus on a restricted variant of this problem, where the input formula is monotone (i.e., there are no negations). A monotone Conjunctive Normal Form (CNF) formula is sufficient for modeling various graph problems, e.g., the vertex covers of a graph. Even for this restricted case there is no known efficient approximation scheme. We show that the classical Spectra technique that is widely used in Network Reliability can be adapted for counting monotone CNF formulas. We prove that the proposed algorithm is logarithmically efficient for random monotone 2-CNF instances. Although we do not prove the efficiency of Spectra for k-CNF where k > 2, our experiments show that it is effective in practice for such formulas as well.