Regular languages are church-rosser congruential

Authors:
Volker Diekert;Manfred Kufleitner;Klaus Reinhardt;Tobias Walter
Affiliations:
Institut für Formale Methoden der Informatik, University of Stuttgart, Germany;Institut für Formale Methoden der Informatik, University of Stuttgart, Germany;Wilhelm-Schickard-Institut für Informatik, University of Tübingen, Germany;Institut für Formale Methoden der Informatik, University of Stuttgart, Germany
Venue:
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Year:
2012

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Abstract

This paper proves a long standing conjecture in formal language theory. It shows that 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 on the other hand it was strongly believed that all regular languages are of this form. This paper solves the conjecture affirmatively by actually proving a more general result.