Construction of regular languages and recognizability of polynomials
Computational Complexity
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.cs/9908018,
title = {Construction of regular languages and recognizability of polynomials},
author = {Michel Rigo},
journal= {arXiv preprint arXiv:cs/9908018},
year = {2007}
}
Comments
11 pages