Rounding Meets Approximate Model Counting

Abstract

AbstractThe 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 $$\textsf{ApproxMC}$$.