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On the k-freeness of morphisms on free monoids. (English) Zbl 0604.20056

A morphism \(h: X\to Y\) between two finitely generated free monoids is k- free if it maps X(k) into Y(k), where \(X(k)=X\setminus X\{w^ k:\) w in \(X\setminus 1\}X\). The author gives necessary conditions for a morphism to be k-free and a finite test to determine whether a morphism h is k- free when it is length uniform from X generated by two symbols.
Reviewer: T.J.Harju

MSC:

20M05 Free semigroups, generators and relations, word problems
20M35 Semigroups in automata theory, linguistics, etc.
20M15 Mappings of semigroups
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