{"id":1143224,"date":"2025-06-27T12:58:59","date_gmt":"2025-06-27T19:58:59","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/?post_type=msr-research-item&p=1143224"},"modified":"2025-06-27T13:05:43","modified_gmt":"2025-06-27T20:05:43","slug":"polysat-word-level-bit-vector-reasoning-in-z3","status":"publish","type":"msr-research-item","link":"https:\/\/www.microsoft.com\/en-us\/research\/publication\/polysat-word-level-bit-vector-reasoning-in-z3\/","title":{"rendered":"PolySAT: Word-level Bit-vector Reasoning in Z3"},"content":{"rendered":"

PolySAT<\/span>\u00a0is a word-level decision procedure supporting bit-precise SMT reasoning over polynomial arithmetic with large bit-vector operations. Addressing challenges of verified software,\u00a0<\/span>PolySAT<\/span>\u00a0integrates the theoretical development of SMT-based calculi with a proof of concept implementation and empirical evaluation. The\u00a0<\/span>PolySAT<\/span>\u00a0calculus extends conflict-driven clause learning modulo theories with two key components: (i) a bit-vector plugin to the equality graph, and (ii) a theory solver for bit-vector arithmetic with non-linear polynomials.\u00a0<\/span>PolySAT<\/span>\u00a0implements dedicated procedures to extract bit-vector intervals from polynomial inequalities. For conflict analysis and resolution,\u00a0<\/span>PolySAT<\/span>\u00a0comes with on-demand lemma generation over non-linear bit-vector arithmetic.\u00a0<\/span>PolySAT<\/span>\u00a0is integrated into the SMT solver\u00a0<\/span>Z3<\/span> and has applications in model checking and smart contract verification where bit-blasting techniques on multipliers\/divisions do not scale.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

PolySAT\u00a0is a word-level decision procedure supporting bit-precise SMT reasoning over polynomial arithmetic with large bit-vector operations. Addressing challenges of verified software,\u00a0PolySAT\u00a0integrates the theoretical development of SMT-based calculi with a proof of concept implementation and empirical evaluation. The\u00a0PolySAT\u00a0calculus extends conflict-driven clause learning modulo theories with two key components: (i) a bit-vector plugin to the equality graph, […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"","msr_chapter":"","msr_edition":"","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"","msr_page_range_start":"47","msr_page_range_end":"69","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"International Conference on Verified Software: Theories, Tools, and Experiments (VSTTE 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