2021
DOI: 10.48550/arxiv.2104.13072
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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 F q , this also permits proving that the associated formal power series are transcendental over F q (X).

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