The purpose of this article is to study the algorithmic complexity of the Besicovitch stability of noisy subshifts of finite type, a notion studied in a previous article [1]. First, we exhibit an unstable aperiodic tiling,and then see how it can serve as a building block to implement several reductions from classical undecidable problems on Turing machines. It will follow that the question of stability of subshifts of finite type is undecidable, and the strongest lower bound we obtain in the arithmetical hierarchy is \(\varvec{\Pi }_2\)-hardness. Lastly, we prove that this decision problem,which requires to quantify over an uncountable set of probability measures,has a \(\varvec{\Pi }_4\) upper bound.

本文的目的是研究有限类型噪声子移的贝西科维奇稳定性的算法复杂性，这是上一篇文章 [1] 中研究的概念。首先，我们展示了一种不稳定的非周期性平铺，然后看看它如何作为构建块来实现图灵机上经典不可判定问题的几种简化。由此可见，有限类型子移的稳定性问题是不可判定的，我们在算术层次中获得的最强下界是\(\varvec{\Pi }_2\) -hardness。最后，我们证明这个决策问题需要量化一组不可数的概率度量，具有\(\varvec{\Pi }_4\)上限。