{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T20:00:15Z","timestamp":1762459215676,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2013,12,4]],"date-time":"2013-12-04T00:00:00Z","timestamp":1386115200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Coalgebras in a Kleisli category yield a generic definition of trace\nsemantics for various types of labelled transition systems. In this paper we\napply this generic theory to generative probabilistic transition systems, short\nPTS, with arbitrary (possibly uncountable) state spaces. We consider the\nsub-probability monad and the probability monad (Giry monad) on the category of\nmeasurable spaces and measurable functions. Our main contribution is that the\nexistence of a final coalgebra in the Kleisli category of these monads is\nclosely connected to the measure-theoretic extension theorem for sigma-finite\npre-measures. In fact, we obtain a practical definition of the trace measure\nfor both finite and infinite traces of PTS that subsumes a well-known result\nfor discrete probabilistic transition systems. Finally we consider two example\nsystems with uncountable state spaces and apply our theory to calculate their\ntrace measures.<\/jats:p>","DOI":"10.2168\/lmcs-9(4:16)2013","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T09:37:51Z","timestamp":1405417071000},"source":"Crossref","is-referenced-by-count":4,"title":["Coalgebraic Trace Semantics for Continuous Probabilistic Transition Systems"],"prefix":"10.46298","volume":"Volume 9, Issue 4","author":[{"given":"Henning","family":"Kerstan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Barbara","family":"K\u00f6nig","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2013,12,4]]},"reference":[{"key":"834:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/859\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/859\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:57:59Z","timestamp":1681243079000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/859"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12,4]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-9(4:16)2013","relation":{"is-same-as":[{"id-type":"arxiv","id":"1310.7417","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1310.7417","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2013,12,4]]},"article-number":"859"}}