License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2012.396
URN: urn:nbn:de:0030-drops-34156
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2012/3415/
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Arnold, André ; Michalewski, Henryk ; Niwinski, Damian

On the separation question for tree languages

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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.

BibTeX - Entry

@InProceedings{arnold_et_al:LIPIcs:2012:3415,
  author =	{Andr{\'e} Arnold and Henryk Michalewski and Damian Niwinski},
  title =	{{On the separation question for tree languages}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{396--407},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{Christoph D{\"u}rr and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2012/3415},
  URN =		{urn:nbn:de:0030-drops-34156},
  doi =		{10.4230/LIPIcs.STACS.2012.396},
  annote =	{Keywords: Alternating automata on infinite trees, Index hierarchy, Separation property}
}

Keywords: Alternating automata on infinite trees, Index hierarchy, Separation property
Collection: 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date: 2012
Date of publication: 24.02.2012

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