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Sur la combinatoire des codes à deux mots. (On the combinatorics of two-word codes). (French) Zbl 0593.20066

Two element codes \(X=\{x,y\}\) are studied, that is, subsets X of a free monoid \(A^*\) which generate a free submonoid \(X^*\). It is shown that if a long enough word w in \(X^*\) has two disjoint X-interpretations then w is a factor of \(x^ n\) or \(y^ n\) or w is a power of \(x^ ny\) or \(xy^ n\) for some n. By disjoint X-interpretations we mean that the word w has two ”covers” in \(X^*\) such that these covers have no common cut points inside w.
Reviewer: T.J.Harju

MSC:

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