How to prove that a sequence is not automatic
How to prove that a sequence is not automatic
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DOI：
10.1016/j.exmath.2021.08.001
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发表时间：
2021-04
影响因子：
0.7
通讯作者：
J. Allouche;J. Shallit;R. Yassawi
中科院分区：
文献类型：
--
作者：
J. Allouche;J. Shallit;R. Yassawi
自动序列具有许多其他序列（特别是非均匀形态序列）不一定共享的属性。在本文中，我们调查了一些不同的方法，可以用来证明一个给定的序列是不是自动的。当序列在有限域F q中取值时，这也允许证明相关的形式幂级数在F q（X）上是超越的。
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 q, this also permits proving that the associated formal power series are transcendental over F q (X).