Fast Converging Anytime Model Counting

TL;DR

This paper introduces PartialKC, an anytime approximate model counting method that uses partial knowledge compilation to efficiently estimate model counts, often converging to exact counts with high accuracy.

Contribution

It presents a novel partial knowledge compilation approach for approximate model counting that converges to exact counts and outperforms existing methods in scalability and accuracy.

Findings

PartialKC achieves higher scalability than prior methods.

It provides unbiased estimates that often converge to exact counts.

Empirical results show competitive performance with exact counters.

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.