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In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid that contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra. A rational set generalizes the notion of rational (regular) language (understood as defined by regular expressions) to monoids that are not necessarily free.

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  • Ensemble rationnel (fr)
  • Rational set (en)
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  • En informatique théorique, plus particulièrement en théorie des automates, un ensemble rationnel dans un monoïde est un élément de la plus petite famille de sous-ensembles de ce monoïde qui contient toutes les parties finies et qui est fermée par union, produit et étoile de Kleene. Les ensembles rationnels interviennent en théorie des automates, en théorie des langages formels et en algèbre. La notion d'ensemble rationnel étend la notion de langage rationnel ou régulier en tant qu'ensemble défini par une expression régulière à des monoïdes qui ne sont pas nécessairement libres. (fr)
  • In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid that contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra. A rational set generalizes the notion of rational (regular) language (understood as defined by regular expressions) to monoids that are not necessarily free. (en)
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  • En informatique théorique, plus particulièrement en théorie des automates, un ensemble rationnel dans un monoïde est un élément de la plus petite famille de sous-ensembles de ce monoïde qui contient toutes les parties finies et qui est fermée par union, produit et étoile de Kleene. Les ensembles rationnels interviennent en théorie des automates, en théorie des langages formels et en algèbre. La notion d'ensemble rationnel étend la notion de langage rationnel ou régulier en tant qu'ensemble défini par une expression régulière à des monoïdes qui ne sont pas nécessairement libres. (fr)
  • In computer science, more precisely in automata theory, a rational set of a monoid is an element of the minimal class of subsets of this monoid that contains all finite subsets and is closed under union, product and Kleene star. Rational sets are useful in automata theory, formal languages and algebra. A rational set generalizes the notion of rational (regular) language (understood as defined by regular expressions) to monoids that are not necessarily free. (en)
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