article

Star-free languages are Church-Rosser congruential

Authors:

Volker Diekert,

Manfred Kufleitner, and

Pascal WeilAuthors Info & Claims

Theoretical Computer Science, Volume 454

Pages 129 - 135

https://doi.org/10.1016/j.tcs.2012.01.028

Published: 01 October 2012 Publication History

Abstract

The class of Church-Rosser congruential languages has been introduced by McNaughton, Narendran, and Otto in 1988. A language L is Church-Rosser congruential (belongs to CRCL), if there is a finite, confluent, and length-reducing semi-Thue system S such that L is a finite union of congruence classes modulo S. To date, it is still open whether every regular language is in CRCL. In this paper, we show that every star-free language is in CRCL. In fact, we prove a stronger statement: for every star-free language L there exists a finite, confluent, and subword-reducing semi-Thue system S such that the total number of congruence classes modulo S is finite and such that L is a union of congruence classes modulo S. The construction turns out to be effective.

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Cited By

Diekert VKufleitner M(2019)A survey on the local divisor techniqueTheoretical Computer Science10.1016/j.tcs.2015.07.008610:PA(13-23)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2015.07.008
(2017)Parikh-reducing ChurchRosser representations for some classes of regular languagesTheoretical Computer Science10.1016/j.tcs.2017.08.009702:C(34-47)Online publication date: 30-Nov-2017
https://dl.acm.org/doi/10.1016/j.tcs.2017.08.009
Diekert VKufleitner MReinhardt KWalter T(2015)Regular Languages Are Church-Rosser CongruentialJournal of the ACM10.1145/280822762:5(1-20)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2808227

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cover image Theoretical Computer Science

Theoretical Computer Science Volume 454, Issue

October, 2012

266 pages

ISSN:0304-3975

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Copyright © Elsevier B.V. © 2012.

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 01 October 2012

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Cited By

Diekert VKufleitner M(2019)A survey on the local divisor techniqueTheoretical Computer Science10.1016/j.tcs.2015.07.008610:PA(13-23)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1016/j.tcs.2015.07.008
(2017)Parikh-reducing ChurchRosser representations for some classes of regular languagesTheoretical Computer Science10.1016/j.tcs.2017.08.009702:C(34-47)Online publication date: 30-Nov-2017
https://dl.acm.org/doi/10.1016/j.tcs.2017.08.009
Diekert VKufleitner MReinhardt KWalter T(2015)Regular Languages Are Church-Rosser CongruentialJournal of the ACM10.1145/280822762:5(1-20)Online publication date: 2-Nov-2015
https://dl.acm.org/doi/10.1145/2808227

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