Model Checking Games for the Quantitative µ-Calculus

Authors Diana Fischer, Erich Grädel, Lukasz Kaiser

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Diana Fischer
Erich Grädel
Lukasz Kaiser

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Diana Fischer, Erich Grädel, and Lukasz Kaiser. Model Checking Games for the Quantitative µ-Calculus. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 301-312, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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.
  • Games
  • logic
  • model checking
  • quantitative logics


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