{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,17]],"date-time":"2022-05-17T12:48:42Z","timestamp":1652791722522},"reference-count":11,"publisher":"Association for Computing Machinery (ACM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[1966,1]]},"abstract":"The theory of finite automata is closely linked with the theory of Kleene's regular expressions. In this paper, two formal systems for the algebraic transformation of regular expressions are developed. Both systems are consistent and complete; i.e., the set of equations derivable within the system equals the set of equations between two regular expressions denoting the same event. One of the systems is based upon the uniqueness of the solution of certain regular expression equations, whereas some facts concerning the representation theory of regular events are used in connection with the other.<\/jats:p>","DOI":"10.1145\/321312.321326","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T11:26:10Z","timestamp":1027769170000},"page":"158-169","source":"Crossref","is-referenced-by-count":181,"title":["Two Complete Axiom Systems for the Algebra of Regular Events"],"prefix":"10.1145","volume":"13","author":[{"given":"Arto","family":"Salomaa","sequence":"first","affiliation":[{"name":"University of Turku, Turku, Finland"}]}],"member":"320","reference":[{"key":"e_1_2_1_1_2","first-page":"1","year":"1965","journal-title":"Appl. Math., Harvard U., Cambridge."},{"key":"e_1_2_1_2_2","first-page":"1","volume-title":"Theory of Computing Machin Design, pp","year":"1960"},{"key":"e_1_2_1_3_2","first-page":"529","volume-title":"Proc. Syrup. Mathematica Theory of Automata","author":"Rzozows L J.A.","year":"1963"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1145\/321239.321249"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1145\/320924.320931"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"GItoN H. tlules to manipulate regular expressions of finite automata. IRE Tans. EC-II (1962) 574-575. GItoN H. tlules to manipulate regular expressions of finite automata. IRE Tans. EC-II (1962) 574-575.","DOI":"10.1109\/TEC.1962.5219404"},{"key":"e_1_2_1_7_2","volume-title":"VEB DeuLscher Verlag der Wissensehaften","author":"Luscmow W.M.","year":"1963"},{"key":"e_1_2_1_8_2","first-page":"3","volume-title":"Princeton U. Press","author":"Iz EN","year":"1956"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1109\/TEC.1960.5221603","volume":"9","author":"Mc NAUGHTON","year":"1960","journal-title":"IRE Trans."},{"key":"e_1_2_1_10_2","unstructured":"IREmO V.N. On defining relations for the algebra of regular events. Ukrain. Mat. 2. 16 (1964) 120-126. (Russian) IREmO V.N. On defining relations for the algebra of regular events. Ukrain. Mat. 2. 16 (1964) 120-126. (Russian)"},{"key":"e_1_2_1_11_2","first-page":"75","author":"Sa LOAA","year":"1964","journal-title":"Ann. Univ. Tubrku., Ser. A I"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/321312.321326","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,2]],"date-time":"2021-03-02T20:08:54Z","timestamp":1614715734000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/321312.321326"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1966,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1966,1]]}},"alternative-id":["10.1145\/321312.321326"],"URL":"http:\/\/dx.doi.org\/10.1145\/321312.321326","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"value":"0004-5411","type":"print"},{"value":"1557-735X","type":"electronic"}],"subject":["Artificial Intelligence","Hardware and Architecture","Information Systems","Control and Systems Engineering","Software"],"published":{"date-parts":[[1966,1]]}}}