{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:23Z","timestamp":1753894403891,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>The author introduced models of linear logic known as ''Interaction Graphs''\nwhich generalise Girard's various geometry of interaction constructions. In\nthis work, we establish how these models essentially rely on a deep connection\nbetween zeta functions and the execution of programs, expressed as a cocycle.\nThis is first shown in the simple case of graphs, before begin lifted to\ndynamical systems. Focussing on probabilistic models, we then explain how the\nnotion of graphings used in Interaction Graphs captures a natural class of\nsub-Markov processes. We then extend the realisability constructions and the\nnotion of zeta function to provide a realisability model of second-order linear\nlogic over the set of all (discrete-time) sub-Markov processes.<\/jats:p>","DOI":"10.46298\/lmcs-20(3:18)2024","type":"journal-article","created":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T05:35:08Z","timestamp":1724909708000},"source":"Crossref","is-referenced-by-count":0,"title":["Zeta Functions and the (Linear) Logic of Markov Processes"],"prefix":"10.46298","volume":"Volume 20, Issue 3","author":[{"given":"Thomas","family":"Seiller","sequence":"first","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2024,8,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14129\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14129\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T05:35:08Z","timestamp":1724909708000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/10303"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(3:18)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2001.11906v6","asserted-by":"subject"},{"id-type":"arxiv","id":"2001.11906v5","asserted-by":"subject"},{"id-type":"arxiv","id":"2001.11906v4","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2001.11906","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2001.11906","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,8,29]]},"article-number":"10303"}}