{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,29]],"date-time":"2026-03-29T15:19:55Z","timestamp":1774797595604,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2006,6]]},"abstract":"<jats:p> Let \u03a3 be a finite alphabet. A set [Formula: see text] of regular languages over \u03a3 is called rational if there exists a finite set [Formula: see text] of regular languages over \u03a3 such that [Formula: see text] is a rational subset of the finitely generated semigroup [Formula: see text] with [Formula: see text] as the set of generators and language concatenation as a product. We prove that for any rational set [Formula: see text] and any regular language R \u2286 \u03a3* it is decidable (1) whether [Formula: see text] or not, and (2) whether [Formula: see text] is finite or not. Possible applications to semistructured databases query processing are discussed. <\/jats:p>","DOI":"10.1142\/s0129054106003954","type":"journal-article","created":{"date-parts":[[2006,6,6]],"date-time":"2006-06-06T11:11:37Z","timestamp":1149592297000},"page":"493-506","source":"Crossref","is-referenced-by-count":5,"title":["MEMBERSHIP AND FINITENESS PROBLEMS FOR RATIONAL SETS OF REGULAR LANGUAGES"],"prefix":"10.1142","volume":"17","author":[{"given":"SERGEY","family":"AFONIN","sequence":"first","affiliation":[{"name":"Institute of Mechanics, Lomonosov Moscow State University, Michurinskij prospekt, 1, Moscow, 119192, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ELENA","family":"KHAZOVA","sequence":"additional","affiliation":[{"name":"Institute of Mechanics, Lomonosov Moscow State University, Michurinskij prospekt, 1, Moscow, 119192, Russian Federation"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf4","volume-title":"Algebraic Theory of Machines, Languages, and Semigroups","author":"Arbib M.","year":"1968"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-005-1262-y"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0000(71)80006-5"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1145\/321495.321505"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.2001.1805"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/BF02572479"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(82)90051-4"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(83)90031-4"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/0304-3975(94)90230-5"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/s00224-005-1255-x"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-3975(03)00377-3"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-16761-7_74"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511662508.004"},{"key":"rf18","volume-title":"Jewels of Formal Language Theory","author":"Salomaa A.","year":"1981"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0017135"},{"key":"rf22","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1051\/ita\/1994283-402771","volume":"28","author":"Simon I.","journal-title":"RAIRO \u2013 Informatique Th\u00e9orique et Applications"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054106003954","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:28:06Z","timestamp":1565191686000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054106003954"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,6]]},"references-count":16,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2006,6]]}},"alternative-id":["10.1142\/S0129054106003954"],"URL":"https:\/\/doi.org\/10.1142\/s0129054106003954","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,6]]}}}