{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:36:10Z","timestamp":1753889770956,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2012,9,20]],"date-time":"2012-09-20T00:00:00Z","timestamp":1348099200000},"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>We study the model-checking problem for a quantitative extension of the modal\nmu-calculus on a class of hybrid systems. Qualitative model checking has been\nproved decidable and implemented for several classes of systems, but this is\nnot the case for quantitative questions that arise naturally in this context.\nRecently, quantitative formalisms that subsume classical temporal logics and\nallow the measurement of interesting quantitative phenomena were introduced. We\nshow how a powerful quantitative logic, the quantitative mu-calculus, can be\nmodel checked with arbitrary precision on initialised linear hybrid systems. To\nthis end, we develop new techniques for the discretisation of continuous state\nspaces based on a special class of strategies in model-checking games and\npresent a reduction to a class of counter parity games.<\/jats:p>","DOI":"10.2168\/lmcs-8(3:21)2012","type":"journal-article","created":{"date-parts":[[2013,11,29]],"date-time":"2013-11-29T08:17:46Z","timestamp":1385713066000},"source":"Crossref","is-referenced-by-count":0,"title":["Model Checking the Quantitative mu-Calculus on Linear Hybrid Systems"],"prefix":"10.46298","volume":"Volume 8, Issue 3","author":[{"given":"Diana","family":"Fischer","sequence":"first","affiliation":[]},{"given":"Lukasz","family":"Kaiser","sequence":"additional","affiliation":[]}],"member":"25203","published-online":{"date-parts":[[2012,9,20]]},"reference":[{"key":"715:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/760\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/760\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T19:55:32Z","timestamp":1681242932000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/760"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,9,20]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-8(3:21)2012","relation":{"is-same-as":[{"id-type":"arxiv","id":"1209.1738","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1209.1738","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2012,9,20]]},"article-number":"760"}}