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When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2008.1352
URN: urn:nbn:de:0030-drops-13525
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Fischer , Diana ; Grädel, Erich ; Kaiser, Lukasz

Model Checking Games for the Quantitative µ-Calculus

22011.FischerDiana.Paper.1352.pdf (0.2 MB)


We investigate quantitative extensions of modal logic and the modal
$mu$-calculus, and study the question whether the tight connection
between logic and games can be lifted from the qualitative logics
to their quantitative counterparts. It turns out that, if the
quantitative $mu$-calculus is defined in an appropriate way
respecting the duality properties between the logical operators,
then its model checking problem can indeed be characterised by a
quantitative variant of parity games. However, these quantitative
games have quite different properties than their classical
counterparts, in particular they are, in general, not positionally
determined. The correspondence between the logic and the games
goes both ways: the value of a formula on a quantitative transition
system coincides with the value of the associated quantitative
game, and conversely, the values of quantitative parity games are
definable in the quantitative $mu$-calculus.

BibTeX - Entry

  author =	{Diana Fischer  and Erich Gr{\"a}del and Lukasz Kaiser},
  title =	{{Model Checking Games for the Quantitative {$mu$}-Calculus}},
  booktitle =	{25th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{301--312},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-06-4},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{1},
  editor =	{Susanne Albers and Pascal Weil},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-13525},
  doi =		{10.4230/LIPIcs.STACS.2008.1352},
  annote =	{Keywords: Games, logic, model checking, quantitative logics}

Keywords: Games, logic, model checking, quantitative logics
Collection: 25th International Symposium on Theoretical Aspects of Computer Science
Issue Date: 2008
Date of publication: 06.02.2008

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