How to prove that a sequence is not automatic

Allouche, J.-P.; Shallit, J. and Yassawi, R. (2021). How to prove that a sequence is not automatic. Expositiones Mathematicae (Early Access).

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, this also permits proving that the associated formal power series are transcendental over F().

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