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- W1975372170 abstract "The class of Church-Rosser congruential languages has been introduced by McNaughton, Narendran, and Otto in 1988. A language L is Church-Rosser congruential (belongs to CRCL), if there is a finite, confluent, and length-reducing semi-Thue system S such that L is a finite union of congruence classes modulo S. To date, it is still open whether every regular language is in CRCL. In this paper, we show that every star-free language is in CRCL. In fact, we prove a stronger statement: For every star-free language L there exists a finite, confluent, and subword-reducing semi-Thue system S such that the total number of congruence classes modulo S is finite and such that L is a union of congruence classes modulo S. The construction turns out to be effective." @default.
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- W1975372170 date "2012-10-01" @default.
- W1975372170 modified "2023-09-27" @default.
- W1975372170 title "Star-free languages are Church–Rosser congruential" @default.
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- W1975372170 doi "https://doi.org/10.1016/j.tcs.2012.01.028" @default.
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