Decidability and k-Regular Sequences
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Date
2020-05
Authors
Krenn, Daniel
Shallit, Jeffrey
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Abstract
In this paper we consider a number of natural decision problems involving k-regular sequences. Specifically, they arise from considering • 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 these decision problems are undecidable.
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Keywords
k-regular sequence, decidability, unsolvability