{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T04:54:57Z","timestamp":1773636897225,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2015,11]]},"abstract":"<jats:p> We search for the largest syntactic semigroups of star-free languages having n left quotients; equivalently, we look for the largest transition semigroups of aperiodic finite automata with n states. We first introduce unitary semigroups generated by transformations that change only one state. In particular, we study unitary-complete semigroups which have a special structure, and show that each maximal unitary semigroup is unitary-complete. For [Formula: see text] we exhibit a unitary-complete semigroup that is larger than any aperiodic semigroup known to date. We then present even larger aperiodic semigroups, generated by transformations that map a non-empty subset of states to a single state; we call such transformations and semigroups semiconstant. We examine semiconstant tree semigroups which have a structure based on full binary trees. The semiconstant tree semigroups are at present the best candidates for largest aperiodic semigroups. <\/jats:p>","DOI":"10.1142\/s0129054115400067","type":"journal-article","created":{"date-parts":[[2016,1,4]],"date-time":"2016-01-04T06:28:46Z","timestamp":1451888926000},"page":"913-931","source":"Crossref","is-referenced-by-count":6,"title":["Large Aperiodic Semigroups"],"prefix":"10.1142","volume":"26","author":[{"given":"Janusz","family":"Brzozowski","sequence":"first","affiliation":[{"name":"David R. Cheriton School of Computer Science, University of Waterloo, Waterloo, ON, Canada N2L 3G1, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marek","family":"Szyku\u0142a","sequence":"additional","affiliation":[{"name":"Institute of Computer Science, University of Wroc\u0142aw, Joliot-Curie 15, PL-50-383 Wroc\u0142aw, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,1,3]]},"reference":[{"issue":"1","key":"p_1","first-page":"71","volume":"15","author":"Brzozowski J.","year":"2010","journal-title":"J. Autom. Lang. Comb."},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054113400133"},{"key":"p_3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(80)90003-3"},{"issue":"2","key":"p_5","first-page":"83","volume":"17","author":"Brzozowski J.","year":"2012","journal-title":"J. Autom. Lang. Comb."},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054112400515"},{"key":"p_8","first-page":"124","volume":"8587","author":"Brzozowski J.","year":"2014","journal-title":"LNCS"},{"key":"p_10","doi-asserted-by":"publisher","DOI":"10.1109\/PGEC.1966.264264"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1007\/BF03025769"},{"key":"p_12","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500026936"},{"key":"p_14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-39274-0_30"},{"key":"p_17","doi-asserted-by":"publisher","DOI":"10.1016\/S0019-9958(65)90108-7"},{"key":"p_18","first-page":"221","volume":"6","author":"Yu S.","year":"2001","journal-title":"J. Autom. Lang. Comb."}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054115400067","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T19:51:59Z","timestamp":1565121119000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054115400067"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11]]},"references-count":12,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2016,1,3]]},"published-print":{"date-parts":[[2015,11]]}},"alternative-id":["10.1142\/S0129054115400067"],"URL":"https:\/\/doi.org\/10.1142\/s0129054115400067","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11]]}}}