Construction of regular languages and recognizability of polynomials
<|reference_start|>Construction of regular languages and recognizability of polynomials: A generalization of numeration system in which the set N of the natural numbers is recognizable by finite automata can be obtained by describing a lexicographically ordered infinite regular language. Here we show that if P belonging to Q[x] is a polynomial such that P(N) is a subset of N then we can construct a numeration system in which the set of representations of P(N) is regular. The main issue in this construction is to setup a regular language with a density function equals to P(n+1)-P(n) for n large enough.<|reference_end|>
@article{rigo1999construction,
    title={Construction of regular languages and recognizability of polynomials},
    author={Michel Rigo},
    journal={arXiv preprint arXiv:cs/9908018},
    year={1999},
    archivePrefix={arXiv},
    eprint={cs/9908018},
    primaryClass={cs.CC}
}