On the separation question for tree languages

André Arnold (1) , Henryk Michalewski (2) , Damian Niwinski (2)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 MIMUW - Faculty of Mathematics, Informatics, and Mechanics [Warsaw]

We show that the separation property fails for the classes Sigma_n of the Rabin-Mostowski index hierarchy of alternating automata on infinite trees. This extends our previous result (obtained with Szczepan Hummel) on the failure of the separation property for the class Sigma_2 (i.e., for co-Buchi sets). It remains open whether the separation property does hold for the classes Pi_n of the index hierarchy. To prove our result, we first consider the Rabin-Mostowski index hierarchy of deterministic automata on infinite words, for which we give a complete answer (generalizing previous results of Selivanov): the separation property holds for Pi_n and fails for Sigma_n-classes. The construction invented for words turns out to be useful for trees via a suitable game.

Mots clés: Alternating automata on infinite trees; Index hierarchy; Separation property

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

André Arnold, Henryk Michalewski, Damian Niwinski. On the separation question for tree languages. STACS'12 (29th Symposium on Theoretical Aspects of Computer Science), Feb 2012, Paris, France. pp.396-407. ⟨hal-00678186⟩