## 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.

### Keywords:

Two element codes; free monoid; X-interpretations
Full Text:

### References:

 [1] Ehrenfeucht, A.; Karhumäki, J.; Rozenberg, G., The (generalized) post correspondence problem with lists consisting of two words is decidable, Theoret. comput. sci., 21, 119-144, (1982) · Zbl 0493.68076 [2] Karhumäki, J., A property of three-element codes, (), 305-313 [3] Karhumäki, J., About intersection of two free monoïds generated by two elements, Semigroup forum, (1984) [4] Lentin, A., Equations dans LES monoïdes libres, (1972), Gauthiers-Villars Paris · Zbl 0258.20058 [5] Lentin, A.; Schützenberger, M.P., A combinatorial problem in the theory of free monoïds, (), 128-144 · Zbl 0221.20076 [6] Le Rest, E.; Le Rest, M., Sur LES relations entre un nombre fini de mots, Thèse de 3ème cycle, (1979), Rouen [7] Le Rest, E.; Le Rest, M., Sur le calcul du monoïde syntaxique d’un sous monoïde finiment engendré, Semigroup forum, 21, 173-185, (1980) · Zbl 0451.20060 [8] Lothaire, M., Combinatorics on words, () · Zbl 1001.68093 [9] Lyndon, R.C.; Schützenberger, M.P., The equation am = bncp in a free group, Michigan math. J., 9, 289-298, (1962) · Zbl 0106.02204 [10] Schützenberger, M.P., A property of finitely generated submonoïds, (), 545-576 · Zbl 0413.20042 [11] Spehner, J.C., Quelques problèmes d’extension, de conjugaison et de présentation des sous-monoïdes d’un monoïde libre, () · Zbl 0468.20048
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.