Rounding Meets Approximate Model Counting

Abstract The problem of model counting, also known as $$\#\textsf{SAT}$$ # SAT , is to compute the number models or satisfying assignments a given Boolean formula F . Model counting fundamental in computer science with wide range applications. In recent years, there has been growing interest using hashing-based techniques for approximate that provide $$(\varepsilon \delta )$$ ( ε , δ ) -guarantees: i.e., count returned within $$(1+\varepsilon 1 + -factor exact confidence at least $$1-\delta $$ - While attain reasonable scalability large enough values $$\delta their severely impacted smaller thereby preventing adoption application domains require estimates high confidence. primary contribution this paper address Achilles heel techniques: we propose novel approach based on rounding allows us achieve significant reduction runtime resulting counter, called $$\textsf{ApproxMC6}$$ ApproxMC 6 (The tool available open-source https://github.com/meelgroup/approxmc ), achieves substantial performance improvement over current state-of-the-art $$\textsf{ApproxMC}$$ particular, our extensive evaluation benchmark suite consisting 1890 instances shows solves 204 more than and $$4\times 4 × speedup