## A characterization of power-free morphisms.(English)Zbl 0572.68066

A word is called k th power-free if it does not contain any non-empty factor $$u^ k$$. A morphism is k th power-free if it preserves k th power-free words. A morphism is power-free if it is k th power-free for every $$k>1$$. We show that it is decidable whether a morphism is power- free; more precisely, we prove that a morphism h is power-free iff: h is a square-free morphism and, for each letter a, the image $$h(a^ 2)$$ is cube-free.

### MSC:

 68Q45 Formal languages and automata 20M35 Semigroups in automata theory, linguistics, etc.

power-free words
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### References:

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