Decidability and k-regular sequences

In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from considering center dot lower and upper bounds on growth rate; in particular boundedness, center dot images, center dot regularity (recognizability by a deterministic finite automaton) of preimages, and center dot factors, such as squares and palindromes, of such sequences. We show that these decision problems are undecidable. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).