Regular Languages are Church-Rosser Congruential

Details Regular Languages are Church-Rosser Congruential Regular Languages are Church-Rosser Congruential

2012-02-06

arxiv.org/abs/1202.1148v1

Computer Science

Formal Languages and Automata Theory

Scientific paper

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.

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