Generalization of automatic sequences for numeration systems on a regular language

Details Generalization of automatic sequences for numeration systems on a regular language Generalization of automatic sequences for numeration systems on a regular language

1999-06-22

arxiv.org/abs/cs/9906017v1

Theoret. Comput. Sci. 244 (2000) 271--281

Computer Science

Computational Complexity

10 pages, 3 figures

Scientific paper

Let L be an infinite regular language on a totally ordered alphabet (A,<). Feeding a finite deterministic automaton (with output) with the words of L enumerated lexicographically with respect to < leads to an infinite sequence over the output alphabet of the automaton. This process generalizes the concept of k-automatic sequence for abstract numeration systems on a regular language (instead of systems in base k). Here, I study the first properties of these sequences and their relations with numeration systems.

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