Numeration systems on a regular language
<|reference_start|>Numeration systems on a regular language: Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of numeration, we show that ultimately periodic sets are recognizable. We also study the translation and the multiplication by constants as well as the order dependence of the recognizability.<|reference_end|>
@article{lecomte1999numeration,
    title={Numeration systems on a regular language},
    author={Pierre B. A. Lecomte, Michel Rigo},
    journal={arXiv preprint arXiv:cs/9903005},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9903005},
    primaryClass={cs.OH}
}