{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T08:43:17Z","timestamp":1648716197093},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[1998,2]]},"abstract":"<jats:p> For a given integer n, we define \u03c9<jats:sup>n<\/jats:sup>-semigroups as a generalization of \u03c9-semigroups for languages of words of length less than \u03c9<jats:sup>n+1<\/jats:sup>. When they are finite, those algebraic structures define the same sets as those recognized by Choueka automata. These sets are also equivalent to regular expressions in which an unary \u03c9 operator standing for the infinite repetition of a language is as free as the Kleene closure operator is. Naturally, the notion of syntactic congruence still works on \u03c9<jats:sup>n<\/jats:sup>-semigroups: among all \u03c9<jats:sup>n<\/jats:sup>-semigroups recognizing a regular language X, there exists an unique \u03c9<jats:sup>n<\/jats:sup>-semigroup of which all others are refinements. <\/jats:p>","DOI":"10.1142\/s0218196798000028","type":"journal-article","created":{"date-parts":[[2003,7,31]],"date-time":"2003-07-31T10:08:41Z","timestamp":1059646121000},"page":"1-21","source":"Crossref","is-referenced-by-count":12,"title":["Automata, Semigroups and Recognizability of Words on Ordinals"],"prefix":"10.1142","volume":"08","author":[{"given":"Nicolas","family":"Bedon","sequence":"first","affiliation":[{"name":"Institut Gaspard Monge, Universit\u00e9 de Marne-la-Vall\u00e9e, 2, rue de la Butte Verte, 93166 Noisy-le-Grand Cedex, France"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"p_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(95)00006-2"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(78)90036-3"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(66)80013-X"},{"key":"p_9","first-page":"3","author":"Muller D.","year":"1963","journal-title":"Proc. Fourth Annual Symp. IEEE"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-16761-7_79"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-16078-7_75"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90108-7"},{"key":"p_17","first-page":"135","author":"Thomas W.","year":"1990","journal-title":"Elsevier"},{"key":"p_18","first-page":"588","author":"Wilke T.","year":"1991","journal-title":"Berlin"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196798000028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:53:33Z","timestamp":1565128413000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196798000028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,2]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1998,2]]}},"alternative-id":["10.1142\/S0218196798000028"],"URL":"https:\/\/doi.org\/10.1142\/s0218196798000028","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,2]]}}}