## Ensembles code-compatibles et une généralisation du théorème de Sardinas-Patterson.(French)Zbl 0574.20053

Author’s abstract: One denotes by $$A^{\infty}$$ the monoid of all finite and infinite words over an alphabet $$A$$. The code-compatibility of a pair $$(X,Y)$$ of subsets of $$A^{\infty}$$ is here defined. A necessary and sufficient condition, which is a generalization of the Sardinas-Patterson theorem [IER Conv. Record 8, 104–108 (1953)], for $$(X,Y)$$ to be code-compatible is established. It is shown that the class of the submonoids of $$A^{\infty}$$ generated by an infinitary code is closed under intersection, and also that, for any two infinitary codes $$X$$ and $$Y$$, $$X^*\cap Y^*=(X\cap Y)^*$$ iff (X,Y) is code-compatible.”

### MSC:

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

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