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On the separation question for tree languages

Authors André Arnold, Henryk Michalewski, Damian Niwinski

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LIPIcs.STACS.2012.396.pdf
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  • Alternating automata on infinite trees
  • Index hierarchy
  • Separation property

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Abstract

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.

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André Arnold, Henryk Michalewski, and Damian Niwinski. On the separation question for tree languages. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 396-407, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012) https://doi.org/10.4230/LIPIcs.STACS.2012.396

Author Details

André Arnold
Henryk Michalewski
Damian Niwinski
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