{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:52:16Z","timestamp":1753894336987,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications<\/jats:p>\n          <jats:p xml:lang=\"en\">Conjecture that any synchronizing automaton with n states has a reset word of length (n - 1)(2) was made by. Cerny in 1964. Notwithstanding the numerous attempts made by various researchers this conjecture hasn't been definitively proven yet. In this paper we study a random automaton that is sampled uniformly at random from the set of all automata with n states and m(n) letters. We show that for m(n) &gt; 18 ln n any random automaton is synchronizing with high probability. For m(n) &gt; n(beta), beta &gt; 1\/2 we also show that any random automaton with high probability satisfies the. Cerny conjecture.<\/jats:p>","DOI":"10.46298\/dmtcs.514","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T21:47:25Z","timestamp":1629755245000},"source":"Crossref","is-referenced-by-count":1,"title":["Synchronizing random automata"],"prefix":"10.46298","volume":"Vol. 12 no. 4","author":[{"given":"Evgeny","family":"Skvortsov","sequence":"first","affiliation":[{"name":"School of Computing Science"}]},{"given":"Yulia","family":"Zaks","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Mechanics Ural State University"}]}],"member":"25203","published-online":{"date-parts":[[2010,1,1]]},"container-title":["Discrete Mathematics &amp; Theoretical Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dmtcs.episciences.org\/514\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dmtcs.episciences.org\/514\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T20:08:33Z","timestamp":1687291713000},"score":1,"resource":{"primary":{"URL":"https:\/\/dmtcs.episciences.org\/514"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,1,1]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/dmtcs.514","relation":{"is-same-as":[{"id-type":"uri","id":"https:\/\/hal.science\/hal-00990454v1","asserted-by":"subject"}]},"ISSN":["1365-8050"],"issn-type":[{"type":"electronic","value":"1365-8050"}],"subject":[],"published":{"date-parts":[[2010,1,1]]},"article-number":"514"}}