{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T01:57:01Z","timestamp":1772243821254,"version":"3.50.1"},"reference-count":0,"publisher":"SAGE Publications","issue":"2-3","license":[{"start":{"date-parts":[[1998,1,1]],"date-time":"1998-01-01T00:00:00Z","timestamp":883612800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[1998,11]]},"abstract":"<jats:p>\n                    Timed automata are among the most widely studied models for real-time systems. Silent transitions, i.e., \u03f5-transitions, have already been proposed in the original paper on timed automata by Alur and Dill [3]. We show that the class TL\n                    <jats:sub>\u03f5<\/jats:sub>\n                    of timed languages recognized by automata with \u03f5-transitions, is more robust and more expressive than the corresponding class TL without \u03f5-transitions. We then focus on \u03f5-transitions without reset, i.e. \u03f5-transitions which do not reset clocks. We propose an algorithm to construct, given a timed automaton, an equivalent one without such transitions. This algorithm is in two steps, it first suppresses the cycles of \u03f5-transitions without reset and then the remaining ones. Then, we prove that a timed automaton such that no \u03f5-transition which resets clocks lies on any directed cycle, can be effectively transformed into a timed automaton without \u03f5transitions. Interestingly, this main result holds under the assumption of non-Zenoness and it is false otherwise. To complete the picture, we exhibit a simple timed automaton with an \u03f5-transition, which resets some clock, on a cycle and which is not equivalent to any \u03f5-free timed automaton. To show this, we develop a promising new technique based on the notion of precise action. This paper presents a synthesis of the two conference communications [9] and [13].\n                  <\/jats:p>","DOI":"10.3233\/fi-1998-36233","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T21:37:55Z","timestamp":1575322675000},"page":"145-182","source":"Crossref","is-referenced-by-count":85,"title":["Characterization of the Expressive Power of Silent Transitions in Timed Automata"],"prefix":"10.1177","volume":"36","author":[{"given":"B\u00e9atrice","family":"B\u00e9rard","sequence":"first","affiliation":[{"name":"LSV, CNRS URA 2236, ENS de Cachan, 61 av. du Pr\u00e9s. Wilson, F-94235 Cachan Cedex, France, email: berard,petit@lsv.ens-cachan.fr"}]},{"given":"Antoine","family":"Petit","sequence":"additional","affiliation":[{"name":"LSV, CNRS URA 2236, ENS de Cachan, 61 av. du Pr\u00e9s. Wilson, F-94235 Cachan Cedex, France, email: berard,petit@lsv.ens-cachan.fr"}]},{"given":"Volker","family":"Diekert","sequence":"additional","affiliation":[{"name":"Inst. f\u00fcr Informatik, Universit\u00e4t Stuttgart, Breitwiesenstr. 20-22, D-70565 Stuttgart, Germany, email: diekert@informatik.uni-stuttgart.de"}]},{"given":"Paul","family":"Gastin","sequence":"additional","affiliation":[{"name":"LIAFA, Universit\u00e9 Paris 7, 2, place Jussieu, F-75251 Paris Cedex 05, France, email: gastin@liafa.jussieu.fr"}]}],"member":"179","published-online":{"date-parts":[[1998,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1998-36233","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-1998-36233","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T06:50:56Z","timestamp":1751352656000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-1998-36233"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1,1]]},"references-count":0,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[1998,11]]}},"alternative-id":["10.3233\/FI-1998-36233"],"URL":"https:\/\/doi.org\/10.3233\/fi-1998-36233","relation":{"is-cited-by":[{"id-type":"doi","id":"10.1007\/978-3-030-25540-4_3","asserted-by":"object"},{"id-type":"doi","id":"10.1007\/978-3-030-29662-9_12","asserted-by":"object"},{"id-type":"doi","id":"10.1007\/978-3-030-29662-9_11","asserted-by":"object"}]},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1,1]]}}}