In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from - lower and upper bounds on growth rate; in particular boundedness, - images, - regularity (recognizability by a deterministic finite automaton) of preimages, and - factors, such as squares and palindromes of such sequences. We show that the decision problems are undecidable.

中文翻译：

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可判定性和 k-正则序列

在本文中，我们考虑了许多涉及 k 正则序列的自然决策问题。具体来说，它们来自 - 增长率的下限和上限；特别是有界性， - 图像， - 原像的规律性（确定性有限自动机的可识别性），以及 - 因素，例如此类序列的平方和回文。我们证明决策问题是不可判定的。