How to prove that a sequence is not automatic

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 ${\mathbb{F}}_q$, this also permits proving that the associated formal power series are transcendental over ${\mathbb{F}}_q(X)$.