{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T03:40:03Z","timestamp":1713670803293},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p>Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classification of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a difficult problem in general. A restricted problem, also of significant interest, is to ask this question for unary automatic presentations: automatic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally finite, but non-finitely generated unary FA-presentable semigroups may be infinite. Every unary FA-presentable semigroup satisfies some Burnside identity. We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classification is given of the unary FA-presentable completely simple semigroups.<\/jats:p>","DOI":"10.1142\/s0218196712500385","type":"journal-article","created":{"date-parts":[[2012,3,5]],"date-time":"2012-03-05T22:33:17Z","timestamp":1330986797000},"page":"1250038","source":"Crossref","is-referenced-by-count":1,"title":["UNARY FA-PRESENTABLE SEMIGROUPS"],"prefix":"10.1142","volume":"22","author":[{"given":"ALAN J.","family":"CAIN","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica, Universidade do Porto, Rua do Campo Alegre 687, 4169\u2013007 Porto, Portugal"}]},{"given":"NIK","family":"RU\u0160KUC","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS, UK"}]},{"given":"RICHARD M.","family":"THOMAS","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, UK"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88282-4_15"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2009.02.005"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-009-9216-4"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.2307\/2372706"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1090\/surv\/007.1"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.03.035"},{"key":"rf8","volume-title":"Introduction to Automata Theory, Languages, and Computation","author":"Hopcroft J. E.","year":"1979"},{"key":"rf9","series-title":"London Mathematical Society Monographs (N. S.)","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198511946.001.0001","volume-title":"Fundamentals of Semigroup Theory","volume":"12","author":"Howie J. M.","year":"1995"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-60178-3_93"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2010.12.045"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.04.015"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196712500385","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,21]],"date-time":"2024-04-21T03:20:26Z","timestamp":1713669626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196712500385"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S0218196712500385"],"URL":"https:\/\/doi.org\/10.1142\/s0218196712500385","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}