Rounding Meets Approximate Model Counting

Jiong Yang, Kuldeep S. Meel

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.