{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:15:51Z","timestamp":1750306551451,"version":"3.41.0"},"reference-count":14,"publisher":"Association for Computing Machinery (ACM)","issue":"5","license":[{"start":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T00:00:00Z","timestamp":1446422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"crossref","award":["DI 435\/5-1"],"award-info":[{"award-number":["DI 435\/5-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"crossref"}]},{"name":"NUS"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2015,11,2]]},"abstract":"<jats:p>\n            This article shows a general result about finite monoids and weight reducing string rewriting systems. As a consequence it proves a long standing conjecture in formal language theory: All regular languages are Church-Rosser congruential. The class of Church-Rosser congruential languages was introduced by McNaughton, Narendran, and Otto in 1988. A language\n            <jats:italic>L<\/jats:italic>\n            is Church-Rosser congruential if there exists a finite, confluent, and length-reducing semi-Thue system\n            <jats:italic>S<\/jats:italic>\n            such that\n            <jats:italic>L<\/jats:italic>\n            is a finite union of congruence classes modulo\n            <jats:italic>S<\/jats:italic>\n            . It was known that there are deterministic linear context-free languages which are not Church-Rosser congruential, but the conjecture was that all regular languages are of this form. The article offers a stronger statement: A language is regular if and only if it is strongly Church-Rosser congruential. It is the journal version of the conference abstract which was presented at ICALP 2012.\n          <\/jats:p>","DOI":"10.1145\/2808227","type":"journal-article","created":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T17:09:35Z","timestamp":1446484175000},"page":"1-20","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Regular Languages Are Church-Rosser Congruential"],"prefix":"10.1145","volume":"62","author":[{"given":"Volker","family":"Diekert","sequence":"first","affiliation":[{"name":"University of Stuttgart"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manfred","family":"Kufleitner","sequence":"additional","affiliation":[{"name":"University of Stuttgart"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Klaus","family":"Reinhardt","sequence":"additional","affiliation":[{"name":"University of T\u00fcbingen"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tobias","family":"Walter","sequence":"additional","affiliation":[{"name":"University of Stuttgart"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,11,2]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"crossref","unstructured":"R. Book and F. Otto. 1993. String-Rewriting Systems. Springer.   R. Book and F. Otto. 1993. String-Rewriting Systems. Springer.","DOI":"10.1007\/978-1-4613-9771-7"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1997.2681"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2006.07.002"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-31585-5_19"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2012.01.028"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.5555\/60452"},{"key":"e_1_2_1_7_1","series-title":"Encyclopedia of Mathematics and its Applications Series","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511566097","volume-title":"Combinatorics on Words","author":"Lothaire M.","year":"1997","unstructured":"M. Lothaire . 1983. Combinatorics on Words . Encyclopedia of Mathematics and its Applications Series , vol. 17 , Addison-Wesley, Reading, MA . (Reprinted by Cambridge University Press , 1997 .) M. Lothaire. 1983. Combinatorics on Words. Encyclopedia of Mathematics and its Applications Series, vol. 17, Addison-Wesley, Reading, MA. (Reprinted by Cambridge University Press, 1997.)"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/42282.42284"},{"volume-title":"Lectures on algebras and triple systems. Tech. rep","author":"Meyberg K.","key":"e_1_2_1_9_1","unstructured":"K. Meyberg . 1972. Lectures on algebras and triple systems. Tech. rep ., University of Virginia , Charlottesville. K. Meyberg. 1972. Lectures on algebras and triple systems. Tech. rep., University of Virginia, Charlottesville."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ic.2004.09.003"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.5555\/647860.736304"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/800161.805168"},{"key":"e_1_2_1_15_1","unstructured":"K. Reinhardt and D. Th\u00e9rien. 2003. Some more regular languages that are Church Rosser congruential. In 13. Theorietag Automaten und Formale Sprachen Herrsching Germany. 97--103.  K. Reinhardt and D. Th\u00e9rien. 2003. Some more regular languages that are Church Rosser congruential. In 13. Theorietag Automaten und Formale Sprachen Herrsching Germany. 97--103."},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0890-5401(03)00035-X"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2808227","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2808227","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T06:12:41Z","timestamp":1750227161000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2808227"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,2]]},"references-count":14,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2015,11,2]]}},"alternative-id":["10.1145\/2808227"],"URL":"https:\/\/doi.org\/10.1145\/2808227","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"type":"print","value":"0004-5411"},{"type":"electronic","value":"1557-735X"}],"subject":[],"published":{"date-parts":[[2015,11,2]]},"assertion":[{"value":"2012-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-07-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-11-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}