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Title: Regular languages are Church-Rosser congruential
Authors: Diekert, Volker
Kufleitner, Manfred
Reinhardt, Klaus
Walter, Tobias
Keywords: Church-Rosser system
Local divisor
Regular language
Semigroup
String rewriting
Issue Date: 2015
Publisher: © the Authors. Published by ACM
Citation: DIEKERT, V. ...et al., 2015. Regular languages are Church-Rosser congruential. Journal of the ACM, 62(5): 39.
Abstract: © 2015 ACM 0004-5411/2015/10-ART32 15.00. 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 L is Church-Rosser congruential if there exists a finite, confluent, and length-reducing semi-Thue system S such that L is a finite union of congruence classes modulo S. 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.
Description: © ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Journal of the ACM, 62(5): 39. https://doi.org/10.1145/2808227
Sponsor: M. Kufleitner was supported by the German Research Foundation (DFG) under grant DI 435/5-1
Version: Accepted for publication
DOI: 10.1145/2808227
URI: https://dspace.lboro.ac.uk/2134/31954
Publisher Link: https://doi.org/10.1145/2808227
ISSN: 0004-5411
Appears in Collections:Published Articles (Computer Science)

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