Regular Languages are Church-Rosser Congruential
Formal Languages and Automata Theory
2012-02-07 v1
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 language are of this form. Actually, this paper proves a more general result.
Cite
@article{arxiv.1202.1148,
title = {Regular Languages are Church-Rosser Congruential},
author = {Volker Diekert and Manfred Kufleitner and Klaus Reinhardt and Tobias Walter},
journal= {arXiv preprint arXiv:1202.1148},
year = {2012}
}