{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T11:10:05Z","timestamp":1751368205709,"version":"3.41.0"},"reference-count":0,"publisher":"SAGE Publications","issue":"3-4","license":[{"start":{"date-parts":[[2009,5,1]],"date-time":"2009-05-01T00:00:00Z","timestamp":1241136000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2009,5]]},"abstract":"<jats:p> Computing short regular expressions equivalent to a given finite automaton is a hard task. In this work we present a class of acyclic automata for which it is possible to obtain in time O(n $^{2}$ log n) an equivalent regular expression of size O(n). A characterisation of this class is made using properties of the underlying digraphs that correspond to the series-parallel digraphs class. Using this characterisation we present an algorithm for the generation of automata of this class and an enumerative formula for the underlying digraphs with a given number of vertices. <\/jats:p>","DOI":"10.3233\/fi-2009-0061","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T03:36:49Z","timestamp":1575344209000},"page":"611-629","source":"Crossref","is-referenced-by-count":6,"title":["Series-Parallel Automata and Short Regular Expressions"],"prefix":"10.1177","volume":"91","author":[{"given":"Nelma","family":"Moreira","sequence":"first","affiliation":[{"name":"DCC-FC & LIACC, Universidade do Porto, R. do Campo Alegre 1021\/1055, 4169-007 Porto, Portugal. {nam,rvr}@ncc.up.pt"}]},{"given":"Rog\u00e9rio","family":"Reis","sequence":"additional","affiliation":[{"name":"DCC-FC & LIACC, Universidade do Porto, R. do Campo Alegre 1021\/1055, 4169-007 Porto, Portugal. {nam,rvr}@ncc.up.pt"}]}],"member":"179","published-online":{"date-parts":[[2009,5,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-0061","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-0061","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,1]],"date-time":"2025-07-01T10:50:30Z","timestamp":1751367030000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2009-0061"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5]]},"references-count":0,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2009,5]]}},"alternative-id":["10.3233\/FI-2009-0061"],"URL":"https:\/\/doi.org\/10.3233\/fi-2009-0061","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"type":"print","value":"0169-2968"},{"type":"electronic","value":"1875-8681"}],"subject":[],"published":{"date-parts":[[2009,5]]}}}