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Transfinite Extension of the Mu-Calculus

  • Julian Bradfield
  • Jacques Duparc
  • Sandra Quickert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3634)

Abstract

In [1] Bradfield found a link between finite differences formed by Σ\(^{\rm 0}_{\rm 2}\) sets and the mu-arithmetic introduced by Lubarski [7]. We extend this approach into the transfinite: in allowing countable disjunctions we show that this kind of extended mu-calculus matches neatly to the transfinite difference hierarchy of Σ\(^{\rm 0}_{\rm 2}\) sets. The difference hierarchy is intimately related to parity games. When passing to infinitely many priorities, it might not longer be true that there is a positional winning strategy. However, if such games are derived from the difference hierarchy, this property still holds true.

Keywords

Winning Strategy Game Tree Positional Strategy Winning Region Parity Game 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Julian Bradfield
    • 1
  • Jacques Duparc
    • 2
  • Sandra Quickert
    • 1
  1. 1.Laboratory for Foundations of Computer ScienceUniversity of Edinburgh 
  2. 2.Ecole des HECUniversité de Lausanne 

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