{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,22]],"date-time":"2024-07-22T22:39:20Z","timestamp":1721687960138},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2003,12]]},"abstract":"<jats:p> Finite Deterministic Cover Automata (DFCA) can be obtained from Deterministic Finite Automata (DFA) using the similarity relation and a method of merging similar states. The DFCA minimization procedure can yield different results depending on the order of merging the similar states, because the minimal DFCA for a finite language is in general not unique. <\/jats:p><jats:p> We count the number of minimal DFCA that can be obtained from a given minimal DFA with n states by merging the similar states in the given DFA. We compute an upper-bound for this number and prove that in the worst case, it is n-1 for an unary alphabet, and [Formula: see text] for a non-unary alphabet. We prove that this upper-bound is reached, i.e., for any given positive integer n one can construct a minimal DFA with n states, which has the number of minimal DFCA obtained by merging similar states equal to this maximum expression. <\/jats:p>","DOI":"10.1142\/s0129054103002138","type":"journal-article","created":{"date-parts":[[2003,12,19]],"date-time":"2003-12-19T00:51:21Z","timestamp":1071795081000},"page":"995-1006","source":"Crossref","is-referenced-by-count":3,"title":["COUNTING THE NUMBER OF MINIMAL DFCA OBTAINED BY MERGING STATES"],"prefix":"10.1142","volume":"14","author":[{"given":"CEZAR","family":"C\u00c2MPEANU","sequence":"first","affiliation":[{"name":"Department of Mathematics and Computer Science,  University of Prince Edward Island, Charlottetown, Prince Edward Island,  C1A 4P3, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ANDREI","family":"P\u0102UN","sequence":"additional","affiliation":[{"name":"Department of Computer Science,  University of Western Ontario, London, Ontario, N6A 5B7, Canada"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0129054102000960"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/0219069"},{"key":"rf5","volume-title":"Introduction to Automata Theory, Languages and Computation","author":"Hopcroft J. E.","year":"1979"},{"key":"rf8","volume-title":"Formal Languages","author":"Salomaa A.","year":"1973"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59136-5_2"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054103002138","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T11:25:44Z","timestamp":1565177144000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054103002138"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12]]},"references-count":5,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2003,12]]}},"alternative-id":["10.1142\/S0129054103002138"],"URL":"https:\/\/doi.org\/10.1142\/s0129054103002138","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12]]}}}