On the Enumerative Sequences of Regular Languages on k Symbols

Authors:
Marie-Pierre Béal;Dominique Perrin
Affiliations:
-;-
Venue:
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Year:
2002

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Abstract

The main result is a characterization of enumerative sequences of regular languages on k symbols. We prove that a sequence is the generating series s(z) of a regular language on k symbols if and only if it is the generating series of a language over a k-letter alphabet and if both series s(z) and (kz)* - s(z) are regular. The proof uses transformations on linear representations called inductions.