{"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/bit-vector-model-counting-using-statistical","title":"Bit-Vector Model Counting using Statistical Estimation","arxiv_id":"1712.07770","date":"2017-12-21","proceeding":null,"authors":["Seonmo Kim","Stephen McCamant"],"abstract":"Approximate model counting for bit-vector SMT formulas (generalizing \\#SAT)\nhas many applications such as probabilistic inference and quantitative\ninformation-flow security, but it is computationally difficult. Adding random\nparity constraints (XOR streamlining) and then checking satisfiability is an\neffective approximation technique, but it requires a prior hypothesis about the\nmodel count to produce useful results. We propose an approach inspired by\nstatistical estimation to continually refine a probabilistic estimate of the\nmodel count for a formula, so that each XOR-streamlined query yields as much\ninformation as possible. We implement this approach, with an approximate\nprobability model, as a wrapper around an off-the-shelf SMT solver or SAT\nsolver. Experimental results show that the implementation is faster than the\nmost similar previous approaches which used simpler refinement strategies. The\ntechnique also lets us model count formulas over floating-point constraints,\nwhich we demonstrate with an application to a vulnerability in differential\nprivacy mechanisms.","url_abs":"http://arxiv.org/abs/1712.07770v1","url_pdf":"http://arxiv.org/pdf/1712.07770v1.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":"bit-vector-model-counting-using-statistical","repo_url":"https://github.com/seonmokim/SearchMC","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"model","task_name":"model"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}