{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:17:41Z","timestamp":1759637861135},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,6]]},"abstract":"<jats:p> A set is called recurrent if its minimal automaton is strongly connected and birecurrent if it is recurrent as well as reversal. We prove a series of results concerning birecurrent sets. It is already known that any birecurrent set is completely reducible (that is, such that the minimal representation of its characteristic series is completely reducible). The main result of this paper characterizes completely reducible sets as linear combinations of birecurrent sets <\/jats:p>","DOI":"10.1142\/s0218196718500285","type":"journal-article","created":{"date-parts":[[2018,4,12]],"date-time":"2018-04-12T09:10:40Z","timestamp":1523524240000},"page":"613-652","source":"Crossref","is-referenced-by-count":1,"title":["Birecurrent sets"],"prefix":"10.1142","volume":"28","author":[{"given":"Francesco","family":"Dolce","sequence":"first","affiliation":[{"name":"Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada"}]},{"given":"Dominique","family":"Perrin","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France"}]},{"given":"Antonio","family":"Restivo","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica e Informatica, Universit\u00e0 degli Studi di Palermo, Italy"}]},{"given":"Christophe","family":"Reutenauer","sequence":"additional","affiliation":[{"name":"Laboratoire de Combinatoire et d\u2019Informatique, Math\u00e9matique, Universit\u00e9 du Qu\u00e9bec \u00e0 Montr\u00e9al, Canada"}]},{"given":"Giuseppina","family":"Rindone","sequence":"additional","affiliation":[{"name":"Laboratoire d\u2019Informatique Gaspard-Mong\u00e9, Universit\u00e9 Paris-Est, France"}]}],"member":"219","published-online":{"date-parts":[[2018,6,28]]},"reference":[{"key":"S0218196718500285BIB001","doi-asserted-by":"publisher","DOI":"10.1145\/322326.322334"},{"key":"S0218196718500285BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139195768"},{"key":"S0218196718500285BIB003","volume-title":"Encyclopedia of Mathematics and its Applications","volume":"137","author":"Berstel J.","year":"2011"},{"key":"S0218196718500285BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196792000232"},{"key":"S0218196718500285BIB005","volume-title":"Automata, Languages, and Machines","author":"Eilenberg S.","year":"1974"},{"key":"S0218196718500285BIB006","doi-asserted-by":"publisher","DOI":"10.24033\/bsmf.1857"},{"key":"S0218196718500285BIB007","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196713400158"},{"key":"S0218196718500285BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574174"},{"key":"S0218196718500285BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02676657"},{"key":"S0218196718500285BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/b104443"},{"key":"S0218196718500285BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139195218"},{"key":"S0218196718500285BIB014","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177704860"},{"key":"S0218196718500285BIB015","doi-asserted-by":"publisher","DOI":"10.1051\/ita\/1985190201651"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500285","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:45:49Z","timestamp":1565120749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500285"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6]]},"references-count":13,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2018,6,28]]},"published-print":{"date-parts":[[2018,6]]}},"alternative-id":["10.1142\/S0218196718500285"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500285","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,6]]}}}