{"paper":{"title":"Value Functions as Supermartingale Certificates","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.LO"],"primary_cat":"cs.LG","authors_text":"Agust\\'in Mart\\'inez-Su\\~n\\'e, Alessandro Abate, Daniel Contro, Diptarko Roy, Mirco Giacobbe","submitted_at":"2026-05-29T16:39:02Z","abstract_excerpt":"Certification methods for stochastic systems provide sufficient proof rules, based on real-valued supermartingale certificates, to determine the almost-sure satisfaction of $\\omega$-regular properties (and therefore of linear temporal logic) over general state spaces, encompassing both countably infinite and continuous state spaces. Conversely, reinforcement learning (RL) methods for $\\omega$-regular tasks have received considerable attention, but they typically lack formal guarantees that the learned policy satisfies the specification, except possibly for finite state and action spaces. We br"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.31524","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.31524/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}