Separating Regular Languages by Piecewise Testable and Unambiguous Languages
Résumé
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from another class. We discuss the separation problem for regular languages. We give a PTIME algorithm to check whether two given regular languages are separable by a piecewise testable language, that is, whether a B\Sigma_1(<) sentence can witness that the languages are disjoint. The proof refines an algebraic argument from Almeida and the third author. When separation is possible, we also express a separator by saturating one of the original languages by a suitable congruence. Following the same line, we show that one can as well decide whether two regular languages can be separated by an unambiguous language, albeit with a higher complexity.
Origine : Fichiers produits par l'(les) auteur(s)
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