{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T20:21:34Z","timestamp":1751660494456},"reference-count":22,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:p> We show that it is decidable whether a transitive mixed linear relation has an \u03c9-chain. Using this result, we study a number of liveness verification problems for generalized timed automata within a unified framework. More precisely, we prove that (1) the mixed linear liveness problem for a timed automaton with dense clocks, reversal-bounded counters, and a free counter is decidable, and (2) the Presburger liveness problem for a timed automaton with discrete clocks, reversal-bounded counters, and a pushdown stack is decidable. <\/jats:p>","DOI":"10.1142\/s0129054102001539","type":"journal-article","created":{"date-parts":[[2002,11,21]],"date-time":"2002-11-21T05:17:37Z","timestamp":1037855857000},"page":"911-936","source":"Crossref","is-referenced-by-count":3,"title":["THE EXISTENCE OF \u03c9-CHAINS FOR TRANSITIVE MIXED LINEAR RELATIONS AND  ITS APPLICATIONS"],"prefix":"10.1142","volume":"13","author":[{"given":"ZHE","family":"DANG","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Computer Science, Washington State University, Pullman, Washington 99164, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"OSCAR H.","family":"IBARRA","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  University of California, Santa Barbara, California 93106, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1993.1024"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90010-8"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1145\/174644.174651"},{"key":"p_4","first-page":"113","author":"Ball T.","year":"2000","journal-title":"Berlin"},{"key":"p_5","first-page":"135","author":"Bouajjani A.","year":"1997","journal-title":"Berlin"},{"key":"p_6","first-page":"64","author":"Bouajjani A.","year":"1995","journal-title":"Berlin"},{"key":"p_7","first-page":"262","author":"Comon H.","year":"2000","journal-title":"Berlin"},{"key":"p_8","first-page":"242","author":"Comon H.","year":"1999","journal-title":"Berlin"},{"key":"p_9","first-page":"506","author":"Dang Z.","year":"2001","journal-title":"Berlin"},{"key":"p_10","first-page":"69","author":"Dang Z.","year":"2000","journal-title":"Berlin"},{"key":"p_11","first-page":"132","author":"Dang Z.","year":"2001","journal-title":"Berlin"},{"key":"p_12","first-page":"132","author":"Dang Z.","year":"2001","journal-title":"Berlin"},{"key":"p_13","first-page":"324","author":"Esparza J.","year":"2001","journal-title":"Berlin"},{"key":"p_14","first-page":"9","author":"Finkel A.","year":"2000","journal-title":"Electronic Notes in Theoretical Computer Science"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(81)90028-3"},{"key":"p_16","first-page":"265","author":"Henzinger T. A.","year":"1995","journal-title":"Berlin"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1994.1045"},{"key":"p_19","doi-asserted-by":"publisher","DOI":"10.1145\/322047.322058"},{"key":"p_21","doi-asserted-by":"publisher","DOI":"10.1007\/s100090050010"},{"key":"p_22","first-page":"529","author":"Laroussinie F.","year":"1995","journal-title":"Berlin"},{"key":"p_23","first-page":"33","author":"Raskin J.","year":"1997","journal-title":"Berlin"},{"key":"p_25","first-page":"694","author":"Wilke T.","year":"1994","journal-title":"Berlin"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054102001539","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:34:14Z","timestamp":1565177654000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054102001539"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":22,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2002,12]]}},"alternative-id":["10.1142\/S0129054102001539"],"URL":"https:\/\/doi.org\/10.1142\/s0129054102001539","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}