Résumé
Dans cet article, on étudie les rapports entre la principauté d'une famille de langages en tant que cylindre et en tant que famille fermée par application séquentielle gauche (gsm) inverse. Pour cela on considère les familles de langages closes pour les opérations de cylindre et les gsm inverses. On montre qu'une telle famille est principale en tant que cylindre seulement si elle est principale vis à vis des gsm inverses, mais que l'inverse n'est pas vrai. Cependant, si l'on se restreint aux familles de langages vérifiant une propriété de clôture que l'on explicite, on obtient cette réciproque.
Abstract
In this paper, the relations between the principality of a family of languages as a cylinder and its principality as family closed under inverse gsm mappings are studied. For that purpose, the families of languages closed under the operations of cylinder and under inverse gsm mappings are considered. It is shown that such a family is a principal cylinder only if it is principal through the operation of inverse gsm mapping, but that the converse is not true. However, the converse is true for the families satisfying a closure property given here.
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Autebert, JM. Opérations de cylindre et applications séquentielles gauches inverses. Acta Informatica 11, 241–258 (1979). https://doi.org/10.1007/BF00289070
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DOI: https://doi.org/10.1007/BF00289070