Separating without any ambiguity

Thomas Place (1) , Marc Zeitoun (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

We investigate a standard operator on classes of languages: unambiguous polynomial closure. We show that if C is a class of regular languages having some mild properties, the membership problem for its unambiguous polynomial closure UPol(C) reduces to the same problem for C. We give a new, self-contained and elementary proof of this result. We also show that unambiguous polynomial closure coincides with alternating left and right deterministic closure. Finally, if additionally C is finite, we show that the separation and covering problems are decidable for UPol(C).

Mots clés: Regular languages; Separation problem; Decidable characterizations

Domaines: Théorie et langage formel [cs.FL]

Thomas Place, Marc Zeitoun. Separating without any ambiguity. 45th International Colloquium on Automata, Languages and Programming, ICALP 2018, Jul 2018, Prague, Czech Republic. ⟨10.4230/LIPIcs.ICALP.2018⟩. ⟨hal-01798847⟩