A characterization of overlap-free morphisms
Discrete Applied Mathematics
Handbook of formal languages, vol. 1
Characterization of test-sets for overlap-free morphisms
Discrete Applied Mathematics
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
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Finite Test-Sets for Overlap-Free Morphisms
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Fixed points avoiding Abelian k-powers
Journal of Combinatorial Theory Series A
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We address the characterization of finite test-sets for cubefreeness of morphisms between free monoids, that is, the finite sets T such that a morphism f is cube-free if and only if f(T) is cube-free. We first prove that such a finite test-set does not exist for morphisms defined on an alphabet containing at least three letters. Then we prove that for binary morphisms, a set T of cube-free words is a test-set if and only if it contains twelve particular factors. Consequently, a morphism f on {a, b} is cube-free if and only if f(aabbababbabbaabaababaabb) is cube-free (length 24 is optimal). Another consequence is an unpublished result of Leconte: A binary morphism is cube-free if and only if the images of all cube-free words of length 7 are cube-free. We also prove that, given an alphabet A containing at least two letters, the monoid of cube-free endomorphisms on A is not finitely generated.