English

How to prove that a sequence is not automatic

Number Theory 2021-04-28 v1

Abstract

Automatic sequences have many properties that other sequences (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of different methods that can be used to prove that a given sequence is not automatic. When the sequences take their values in the finite field Fq{\mathbb F}_q, this also permits proving that the associated formal power series are transcendental over Fq(X){\mathbb F}_q(X).

Keywords

Cite

@article{arxiv.2104.13072,
  title  = {How to prove that a sequence is not automatic},
  author = {J. -P. Allouche and J. Shallit and R. Yassawi},
  journal= {arXiv preprint arXiv:2104.13072},
  year   = {2021}
}
R2 v1 2026-06-24T01:33:18.691Z