English

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.

Keywords

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}
}