Affiliation:
1. University of Stuttgart
2. University of Tübingen
Abstract
This article shows a general result about finite monoids and weight reducing string rewriting systems. As a consequence it proves a long standing conjecture in formal language theory: 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 the conjecture was that all regular languages are of this form. The article offers a stronger statement: A language is regular if and only if it is strongly Church-Rosser congruential. It is the journal version of the conference abstract which was presented at ICALP 2012.
Funder
German Research Foundation
NUS
Publisher
Association for Computing Machinery (ACM)
Subject
Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software
Reference14 articles.
1. R. Book and F. Otto. 1993. String-Rewriting Systems. Springer. R. Book and F. Otto. 1993. String-Rewriting Systems. Springer.
2. Growing Context-Sensitive Languages and Church–Rosser Languages
3. Pure future local temporal logics are expressively complete for Mazurkiewicz traces
4. V.
Diekert M.
Kufleitner K.
Reinhardt and
T.
Walter
.
2012
a. Regular languages are Church-Rosser congruential. In Proceedings of the International Colloquium on Automata Languages and Programming (ICALP'12) Part II. A. Czumaj K. Mehlhorn A. Pitts and R. Wattenhofer Eds. Lecture Notes in Computer Science Series vol.
7392 Springer-Verlag 177--188. 10.1007/978-3-642-31585-5_19 V. Diekert M. Kufleitner K. Reinhardt and T. Walter. 2012a. Regular languages are Church-Rosser congruential. In Proceedings of the International Colloquium on Automata Languages and Programming (ICALP'12) Part II. A. Czumaj K. Mehlhorn A. Pitts and R. Wattenhofer Eds. Lecture Notes in Computer Science Series vol. 7392 Springer-Verlag 177--188. 10.1007/978-3-642-31585-5_19
5. Star-free languages are Church–Rosser congruential
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献