On the separation question for tree languages
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.
Alternating automata on infinite trees
Index hierarchy
Separation property
396-407
Regular Paper
AndrĂ©
Arnold
AndrĂ© Arnold
Henryk
Michalewski
Henryk Michalewski
Damian
Niwinski
Damian Niwinski
10.4230/LIPIcs.STACS.2012.396
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