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.2015.489
URN: urn:nbn:de:0030-drops-56390
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5639/
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Michalewski, Henryk ; Mio, Matteo

On the Problem of Computing the Probability of Regular Sets of Trees

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Abstract

We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by game automata. In particular this algorithm is applicable to all deterministic automata. We then use the algorithm to prove through examples three properties of measure: (1) there exist regular sets having irrational probability, (2) there exist comeager regular sets having probability 0 and (3) the probability of game languages W_{i,k}, from automata theory, is 0 if k is odd and is 1 otherwise.

BibTeX - Entry

@InProceedings{michalewski_et_al:LIPIcs:2015:5639,
  author =	{Henryk Michalewski and Matteo Mio},
  title =	{{On the Problem of Computing the Probability of Regular Sets of Trees}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{489--502},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Prahladh Harsha and G. Ramalingam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5639},
  URN =		{urn:nbn:de:0030-drops-56390},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.489},
  annote =	{Keywords: regular languages of trees, probability, meta-parity games}
}

Keywords: regular languages of trees, probability, meta-parity games
Collection: 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)
Issue Date: 2015
Date of publication: 14.12.2015

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