Fast Converging Anytime Model Counting

Abstract: Model counting is a fundamental problem which has been influential in many applications, from artificial intelligence to formal verification. Due to the intrinsic hardness of model counting, approximate techniques have been developed to solve real-world instances of model counting. This paper designs a new anytime approach called PartialKC for approximate model counting. The idea is a form of partial knowledge compilation to provide an unbiased estimate of the model count which can converge to the exact count. Our empirical analysis demonstrates that PartialKC achieves significant scalability and accuracy over prior state-of-the-art approximate counters, including satss and STS. Interestingly, the empirical results show that PartialKC reaches convergence for many instances and therefore provides exact model counting performance comparable to state-of-the-art exact counters.