Rounding Meets Approximate Model Counting

Abstract

Abstract The problem of model counting, also known as $$\#\textsf{SAT}$$ , is to compute the number of models or satisfying assignments of a given Boolean formula F . Model counting is a fundamental problem in computer science with a wide range of applications. In recent years, there has been a growing interest in using hashing-based techniques for approximate model counting that provide $$(\varepsilon , \delta )$$ -guarantees: i.e., the count returned is within a $$(1+\varepsilon )$$ -factor of the exact count with confidence at least $$1-\delta $$ . While hashing-based techniques attain reasonable scalability for large enough values of $$\delta $$ , their scalability is severely impacted for smaller values of $$\delta $$ , thereby preventing their adoption in application domains that require estimates with high confidence. The primary contribution of this paper is to address the Achilles heel of hashing-based techniques: we propose a novel approach based on rounding that allows us to achieve a significant reduction in runtime for smaller values of $$\delta $$ . The resulting counter, called $$\textsf{ApproxMC6}$$ (The resulting tool $$\textsf{ApproxMC6}$$ is available open-source at https://github.com/meelgroup/approxmc ), achieves a substantial runtime performance improvement over the current state-of-the-art counter, $$\textsf{ApproxMC}$$ . In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows $$\textsf{ApproxMC6}$$ solves 204 more instances than $$\textsf{ApproxMC}$$ , and achieves a $$4\times $$ speedup over $$\textsf{ApproxMC}$$ .