HAL : hal-00642351, version 1

arXiv : 1111.4300

Fiche détaillée

Récupérer au format BibTeX - EndNote - TEI - RefWorks -

Theoretical Computer Science (2012) to appear

Star-Free Languages are Church-Rosser Congruential

Volker Diekert 1, Manfred Kufleitner 1, Pascal Weil 2

(2012)

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.

1 :	University of Stuttgart
	University of Stuttgart
2 :	Laboratoire Bordelais de Recherche en Informatique (LaBRI)
	CNRS : UMR5800 – Université Sciences et Technologies - Bordeaux I – École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB) – Université Victor Segalen - Bordeaux II

Domaine

:

Informatique/Théorie et langage formel

Mots Clés : String rewriting – Church-Rosser system – star-free language – aperiodic monoid – local divisor

hal-00642351, version 1

http://hal.archives-ouvertes.fr/hal-00642351

oai:hal.archives-ouvertes.fr:hal-00642351

Contributeur : Pascal Weil <>

Soumis le : Jeudi 17 Novembre 2011, 22:37:42

Dernière modification le : Mercredi 18 Janvier 2012, 16:01:31