Regular languages are Church-Rosser congruential

© 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-...

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Main Authors:	Volker Diekert, Manfred Kufleitner, Klaus Reinhardt, Tobias Walter
Format:	Default Article
Published:	2015
Subjects:	Other information and computing sciences not elsewhere classified Church-Rosser system Local divisor Regular language Semigroup String rewriting Information and Computing Sciences not elsewhere classified
Online Access:	https://hdl.handle.net/2134/31954
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id	rr-article-9401993
record_format	Figshare
spelling	rr-article-94019932015-01-01T00:00:00Z Regular languages are Church-Rosser congruential Volker Diekert (7168556) Manfred Kufleitner (4542364) Klaus Reinhardt (290801) Tobias Walter (7168559) Other information and computing sciences not elsewhere classified Church-Rosser system Local divisor Regular language Semigroup String rewriting Information and Computing Sciences not elsewhere classified © 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. 2015-01-01T00:00:00Z Text Journal contribution 2134/31954 https://figshare.com/articles/journal_contribution/Regular_languages_are_Church-Rosser_congruential/9401993 CC BY-NC-ND 4.0
institution	Loughborough University
collection	Figshare
topic	Other information and computing sciences not elsewhere classified Church-Rosser system Local divisor Regular language Semigroup String rewriting Information and Computing Sciences not elsewhere classified
spellingShingle	Other information and computing sciences not elsewhere classified Church-Rosser system Local divisor Regular language Semigroup String rewriting Information and Computing Sciences not elsewhere classified Volker Diekert Manfred Kufleitner Klaus Reinhardt Tobias Walter Regular languages are Church-Rosser congruential
description	© 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.
format	Default Article
author	Volker Diekert Manfred Kufleitner Klaus Reinhardt Tobias Walter
author_facet	Volker Diekert Manfred Kufleitner Klaus Reinhardt Tobias Walter
author_sort	Volker Diekert (7168556)
title	Regular languages are Church-Rosser congruential
title_short	Regular languages are Church-Rosser congruential
title_full	Regular languages are Church-Rosser congruential
title_fullStr	Regular languages are Church-Rosser congruential
title_full_unstemmed	Regular languages are Church-Rosser congruential
title_sort	regular languages are church-rosser congruential
publishDate	2015
url	https://hdl.handle.net/2134/31954
_version_	1800181273551962112

Regular languages are Church-Rosser congruential

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