{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/rounding-meets-approximate-model-counting","title":"Rounding Meets Approximate Model Counting","arxiv_id":"2305.09247","date":"2023-05-16","proceeding":null,"authors":["Jiong Yang","Kuldeep S. Meel"],"abstract":"The problem of model counting, also known as #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 RoundMC, achieves a substantial runtime performance improvement over the current state-of-the-art counter, ApproxMC. In particular, our extensive evaluation over a benchmark suite consisting of 1890 instances shows that RoundMC solves 204 more instances than ApproxMC, and achieves a $4\\times$ speedup over ApproxMC.","url_abs":"https://arxiv.org/abs/2305.09247v1","url_pdf":"https://arxiv.org/pdf/2305.09247v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"rounding-meets-approximate-model-counting","repo_url":"https://github.com/meelgroup/approxmc","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}