Decidability and k-Regular Sequences
Formal Languages and Automata Theory
2022-02-02 v3 Computational Complexity
Discrete Mathematics
Combinatorics
Abstract
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.
Cite
@article{arxiv.2005.09507,
title = {Decidability and k-Regular Sequences},
author = {Daniel Krenn and Jeffrey Shallit},
journal= {arXiv preprint arXiv:2005.09507},
year = {2022}
}