Abstract
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-Thérien 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.
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© 2002 Springer-Verlag Berlin Heidelberg
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Niemann, G., Waldmann, J. (2002). Some Regular Languages That Are Church-Rosser Congruential. In: Kuich, W., Rozenberg, G., Salomaa, A. (eds) Developments in Language Theory. DLT 2001. Lecture Notes in Computer Science, vol 2295. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46011-X_29
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DOI: https://doi.org/10.1007/3-540-46011-X_29
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