How to prove that a sequence is not automatic

Allouche, J.-P.; Shallit, J. and Yassawi, R. (2022). How to prove that a sequence is not automatic. Expositiones Mathematicae, 40(1) pp. 1–22.

DOI: https://doi.org/10.1016/j.exmath.2021.08.001

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 a finite field F$\textit{q}$, this also permits proving that the associated formal power series are transcendental over F$\textit{q}$($\textit{X}$).

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