Existence of finite test-sets for k-power-freeness of uniform morphisms

Authors:
G. Richomme;F. Wlazinski
Affiliations:
LaRIA, Université de Picardie Jules Verne, 33 Rue Saint Leu, 80039 Amiens cedex 01, France;LaRIA, Université de Picardie Jules Verne, 33 Rue Saint Leu, 80039 Amiens cedex 01, France
Venue:
Discrete Applied Mathematics
Year:
2007

Citing 10
Cited 2

A characterization of overlap-free morphisms

Discrete Applied Mathematics
Combinatorics of words

Handbook of formal languages, vol. 1
Characterization of test-sets for overlap-free morphisms

Discrete Applied Mathematics
Some results on k-power-free morphisms

Theoretical Computer Science
Theory of Codes

Theory of Codes
Some non finitely generated monoids of repetition-free endomorphisms

Information Processing Letters
If a D0L Language is k-Power Free then it is Circular

ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
Overlap-free morphisms and finite test-sets

Discrete Applied Mathematics
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)

Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Growth of repetition-free words: a review

Theoretical Computer Science - The art of theory

Note: There are k-uniform cubefree binary morphisms for all k≥0

Discrete Applied Mathematics
Periodicity, repetitions, and orbits of an automatic sequence

Theoretical Computer Science

Quantified Score

Hi-index	0.05

Visualization

Abstract

A challenging problem is to find an algorithm to decide whether a morphism is k-power-free. When k=3, we provide such an algorithm for uniform morphisms showing that in such a case, contrarily to the general case, there exist finite test-sets for k-power-freeness.