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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 = {http://dx.doi.org/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
Seminar:
29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)
Issue Date:
2012
Date of publication:
24.02.2012
