{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:19:02Z","timestamp":1758824342738},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2009,9]]},"abstract":"<jats:p>This paper studies rr-, \u2113r-, r\u2113-, and \u2113\u2113-automatic structures for finitely generated submonoids of monoids presented by confluent rewriting system that are either finite and special or regular and monadic. A new technique is developed that uses an automaton to \"translate\" between words in the original rewriting system and words over the generators for the submonoid. This is applied to show that the submonoid inherits any notion of automatism possessed by the original monoid. Generalizations of results of Otto and Ru\u0161kuc are thus obtained: every finitely generated submonoid of a monoid presented by a confluent finite special rewriting system admits an automatic structure that is simultaneously rr-, \u2113r-, r\u2113-, and \u2113\u2113-automatic; and every finitely generated submonoid of a monoid presented by a confluent regular monadic rewriting system admits an automatic structure that is simultaneously rr- and \u2113\u2113-automatic. These structures are shown to be effectively computable. An algorithm is given to decide whether the monoid presented by a confluent monadic finite rewriting system is \u2113r- or r\u2113-automatic. Finally, these results are applied to yield answers to some hitherto open questions and to recover and generalize established results.<\/jats:p>","DOI":"10.1142\/s0218196709005317","type":"journal-article","created":{"date-parts":[[2009,10,14]],"date-time":"2009-10-14T09:32:19Z","timestamp":1255512739000},"page":"771-790","source":"Crossref","is-referenced-by-count":2,"title":["MONOIDS PRESENTED BY REWRITING SYSTEMS AND AUTOMATIC STRUCTURES FOR THEIR SUBMONOIDS"],"prefix":"10.1142","volume":"19","author":[{"given":"ALAN J.","family":"CAIN","sequence":"first","affiliation":[{"name":"Centro de Matem\u00e1tica da Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-9771-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572789"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(78)90018-2"},{"key":"rf5","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1515\/JGT.2006.027","volume":"9","author":"Cain A. J.","journal-title":"J. Group Theory"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(99)00151-6"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1080\/00927870209342378"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196705002098"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s10587-008-0018-7"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004199003722"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1201\/9781439865699"},{"key":"rf14","volume-title":"Monographs and Textbooks in Pure and Applied Mathematics","volume":"193","author":"Grillet P. A.","year":"1995"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/s002330010161"},{"key":"rf17","volume-title":"Introduction to Automata Theory, Languages, and Computation","author":"Hopcroft J. E.","year":"1979"},{"key":"rf18","series-title":"London Mathematical Society Monographs (New Series)","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":"rf19","first-page":"375","volume":"6","author":"Otto F.","journal-title":"J. Autom. Lang. Comb."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196709005317","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,17]],"date-time":"2024-03-17T03:30:55Z","timestamp":1710646255000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196709005317"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,9]]},"references-count":15,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,9]]}},"alternative-id":["10.1142\/S0218196709005317"],"URL":"https:\/\/doi.org\/10.1142\/s0218196709005317","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,9]]}}}