English

A note on syndeticity, recognizable sets and Cobham's theorem

Formal Languages and Automata Theory 2009-07-06 v1

Abstract

In this note, we give an alternative proof of the following result. Let p, q >= 2 be two multiplicatively independent integers. If an infinite set of integers is both p- and q-recognizable, then it is syndetic. Notice that this result is needed in the classical proof of the celebrated Cobham?s theorem. Therefore the aim of this paper is to complete [13] and [1] to obtain an accessible proof of Cobham?s theorem.

Keywords

Cite

@article{arxiv.0907.0624,
  title  = {A note on syndeticity, recognizable sets and Cobham's theorem},
  author = {M. Rigo and L. Waxweiler},
  journal= {arXiv preprint arXiv:0907.0624},
  year   = {2009}
}
R2 v1 2026-06-21T13:21:06.973Z