{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:37:00Z","timestamp":1753889820237,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2008,4,9]],"date-time":"2008-04-09T00:00:00Z","timestamp":1207699200000},"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>Desharnais, Gupta, Jagadeesan and Panangaden introduced a family of\nbehavioural pseudometrics for probabilistic transition systems. These\npseudometrics are a quantitative analogue of probabilistic bisimilarity.\nDistance zero captures probabilistic bisimilarity. Each pseudometric has a\ndiscount factor, a real number in the interval (0, 1]. The smaller the discount\nfactor, the more the future is discounted. If the discount factor is one, then\nthe future is not discounted at all. Desharnais et al. showed that the\nbehavioural distances can be calculated up to any desired degree of accuracy if\nthe discount factor is smaller than one. In this paper, we show that the\ndistances can also be approximated if the future is not discounted. A key\ningredient of our algorithm is Tarski's decision procedure for the first order\ntheory over real closed fields. By exploiting the Kantorovich-Rubinstein\nduality theorem we can restrict to the existential fragment for which more\nefficient decision procedures exist.<\/jats:p>","DOI":"10.2168\/lmcs-4(2:2)2008","type":"journal-article","created":{"date-parts":[[2008,6,3]],"date-time":"2008-06-03T13:28:43Z","timestamp":1212499723000},"source":"Crossref","is-referenced-by-count":14,"title":["Approximating a Behavioural Pseudometric without Discount for Probabilistic Systems"],"prefix":"10.46298","volume":"Volume 4, Issue 2","author":[{"given":"Franck","family":"van Breugel","sequence":"first","affiliation":[]},{"given":"Babita","family":"Sharma","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8151-2443","authenticated-orcid":false,"given":"James","family":"Worrell","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2008,4,9]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/822\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/822\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:57:00Z","timestamp":1681243020000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/822"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,4,9]]},"references-count":0,"URL":"https:\/\/doi.org\/10.2168\/lmcs-4(2:2)2008","relation":{"is-same-as":[{"id-type":"arxiv","id":"0803.3796","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.0803.3796","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"doi","id":"10.1007\/978-3-642-36742-7_1","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2008,4,9]]},"article-number":"822"}}