License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2013.299
URN: urn:nbn:de:0030-drops-43812
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/4381/
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Fijalkow, Nathanaël ; Pinchinat, Sophie ; Serre, Olivier

Emptiness Of Alternating Tree Automata Using Games With Imperfect Information

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Abstract

We consider the emptiness problem for alternating tree automata,
with two acceptance semantics: classical (all branches are accepted)
and qualitative (almost all branches are accepted). For the classical semantics, the usual technique to tackle this problem relies on a Simulation Theorem which constructs an equivalent non-deterministic automaton from the original alternating one, and then checks emptiness by a reduction to a two-player perfect information game.
However, for the qualitative semantics, no simulation of alternation by means of non-determinism is known.

We give an alternative technique to decide the emptiness problem of alternating tree automata, that does not rely on a Simulation Theorem.
Indeed, we directly reduce the emptiness problem to solving an imperfect information two-player parity game. Our new approach can successfully be applied to both semantics, and yields decidability results with optimal complexity; for the qualitative semantics, the key ingredient in the proof is a positionality result for stochastic games played over infinite graphs.

BibTeX - Entry

@InProceedings{fijalkow_et_al:LIPIcs:2013:4381,
  author =	{Nathana{\"e}l Fijalkow and Sophie Pinchinat and Olivier Serre},
  title =	{{Emptiness Of Alternating Tree Automata Using Games With Imperfect Information}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{299--311},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Anil Seth and Nisheeth K. Vishnoi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4381},
  URN =		{urn:nbn:de:0030-drops-43812},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.299},
  annote =	{Keywords: Alternating Automata, Emptiness checking, Two-player games, Imperfect Information Games}
}

Keywords: Alternating Automata, Emptiness checking, Two-player games, Imperfect Information Games
Collection: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)
Issue Date: 2013
Date of publication: 10.12.2013

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