RAIRO-Theor. Inf. Appl.
Volume 35, Number 5, September October 2001
|Page(s)||437 - 452|
|Published online||15 August 2002|
A test-set for k-power-free binary morphisms
LaRIA, Université de Picardie Jules Verne, 5 rue du Moulin Neuf,
80000 Amiens, France; firstname.lastname@example.org.
Accepted: November 2001
A morphism f is k-power-free if and only if f(w) is k-power-free whenever w is a k-power-free word. A morphism f is k-power-free up to m if and only if f(w) is k-power-free whenever w is a k-power-free word of length at most m. Given an integer k ≥ 2, we prove that a binary morphism is k-power-free if and only if it is k-power-free up to k2. This bound becomes linear for primitive morphisms: a binary primitive morphism is k-power-free if and only if it is k-power-free up to 2k+1
Mathematics Subject Classification: 68R15
Key words: Combinatorics on words / k-power-free words / morphisms / test-sets
© EDP Sciences, 2001
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