Church-Rosser Thue systems and formal languages
Journal of the ACM (JACM)
String-rewriting systems
Handbook of formal languages, vol. 1: word, language, grammar
Handbook of formal languages, vol. 1: word, language, grammar
Handbook of formal languages, vol. 1
Handbook of formal languages, vol. 1
Characterizing Regular Languages with Polynomial Densities
MFCS '92 Proceedings of the 17th International Symposium on Mathematical Foundations of Computer Science
McNaughton families of languages
Theoretical Computer Science
Restarting automata and their relations to the Chomsky hierarchy
DLT'03 Proceedings of the 7th international conference on Developments in language theory
Regular languages are church-rosser congruential
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Star-free languages are Church-Rosser congruential
Theoretical Computer Science
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In 1988 McNaughton et al introduced the class CRCL of Church-Rosser congruential languages as a way to define formal languages by confluent length-reducing string-rewriting systems. As other congruential language classes CRCL is quite limited, although it contains some languages that are not contextfree. In 2000 Niemann has shown that at least each regular language with polynomial density is Church-Rosser congruential. It is still an open question whether the class of regular languages is contained in CRCL. Here we give some families of regular languages of exponential density that are Church-Rosser congruential. More precisely, we show that some shuffle languages, as well as Level 1 of the Straubing-Th茅rien hierarchy, are in CRCL, using a sufficient condition under which a regular language is Church-Rosser congruential. Last, we give a family of group languages that are Church-Rosser congruential, but do not fulfill this condition.