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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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