Generalization of automatic sequences for numeration systems on a regular language
<|reference_start|>Generalization of automatic sequences for numeration systems on a regular language: 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.<|reference_end|>
@article{rigo1999generalization,
    title={Generalization of automatic sequences for numeration systems on a
  regular language},
    author={Michel Rigo},
    journal={Theoret. Comput. Sci. 244 (2000) 271--281},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9906017},
    primaryClass={cs.CC}
}