On the periodicity of morphic words

Authors:
Vesa Halava;Tero Harju;Tomi Kärki;Michel Rigo
Affiliations:
Department of Mathematics, University of Turku, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland;Department of Mathematics, University of Turku, Turku, Finland;Institute of Mathematics, University of Liège, Liège, Belgium
Venue:
DLT'10 Proceedings of the 14th international conference on Developments in language theory
Year:
2010

Citing 2
Cited 1

Automatic Sequences: Theory, Applications, Generalizations

Automatic Sequences: Theory, Applications, Generalizations
Periodicity, repetitions, and orbits of an automatic sequence

Theoretical Computer Science

Enumeration and decidable properties of automatic sequences

DLT'11 Proceedings of the 15th international conference on Developments in language theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

Given a morphism h prolongable on a and an integer p, we present an algorithm that calculates which letters occur infinitely often in congruent positions modulo p in the infinite word hω(a). As a corollary, we show that it is decidable whether a morphic word is ultimately p-periodic. Moreover, using our algorithm we can find the smallest similarity relation such that the morphic word is ultimately relationally p-periodic. The problem of deciding whether an automatic sequence is ultimately weakly R-periodic is also shown to be decidable.