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.


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