{"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/supermartingale-certificates-for-quantitative","title":"Supermartingale Certificates for Quantitative Omega-regular Verification and Control","arxiv_id":"2505.18833","date":"2025-05-24","proceeding":null,"authors":["Thomas A. Henzinger","Kaushik Mallik","Pouya Sadeghi","Đorđe Žikelić"],"abstract":"We present the first supermartingale certificate for quantitative $\\omega$-regular properties of discrete-time infinite-state stochastic systems. Our certificate is defined on the product of the stochastic system and a limit-deterministic B\\\"uchi automaton that specifies the property of interest; hence we call it a limit-deterministic B\\\"uchi supermartingale (LDBSM). Previously known supermartingale certificates applied only to quantitative reachability, safety, or reach-avoid properties, and to qualitative (i.e., probability 1) $\\omega$-regular properties. We also present fully automated algorithms for the template-based synthesis of LDBSMs, for the case when the stochastic system dynamics and the controller can be represented in terms of polynomial inequalities. Our experiments demonstrate the ability of our method to solve verification and control tasks for stochastic systems that were beyond the reach of previous supermartingale-based approaches.","url_abs":"https://arxiv.org/abs/2505.18833v1","url_pdf":"https://arxiv.org/pdf/2505.18833v1.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":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"supermartingale-certificates-for-quantitative","repo_url":"https://github.com/ipouyall/omega-regular-stoch-cert","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}