English

Least periods of k-automatic sequences

Formal Languages and Automata Theory 2012-07-24 v1 Discrete Mathematics

Abstract

Currie and Saari initiated the study of least periods of infinite words, and they showed that every integer n >= 1 is a least period of the Thue-Morse sequence. We generalize this result to show that the characteristic sequence of least periods of a k-automatic sequence is (effectively) k-automatic. Through an implementation of our construction, we confirm the result of Currie and Saari, and we obtain similar results for the period-doubling sequence, the Rudin-Shapiro sequence, and the paperfolding sequence.

Keywords

Cite

@article{arxiv.1207.5450,
  title  = {Least periods of k-automatic sequences},
  author = {Daniel Goc and Jeffrey Shallit},
  journal= {arXiv preprint arXiv:1207.5450},
  year   = {2012}
}