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Describing the Wadge Hierarchy for the Alternation Free Fragment of μ-Calculus (I)

The Levels Below ω1
  • Jacques Duparc
  • Alessandro Facchini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5028)

Abstract

The height of the Wadge Hierarchy for the Alternation Free Fragment of μ-calculus is known to be at least ε 0. It was conjectured that the height is exactly ε 0. We make a first step towards the proof of this conjecture by showing that there is no \(\Delta^\mu_{2}\) definable set in between the levels ω ω and ω 1 of the Wadge Hierarchy of Borel Sets.

Keywords

μ-calculus Wadge games topological complexity parity games weakly alternating automata 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jacques Duparc
    • 1
  • Alessandro Facchini
    • 1
    • 2
  1. 1.Faculty of Business and Economics - ISIUniversity of LausanneLausanne 
  2. 2.LaBRIUniversity of Bordeaux 1Talence cedex 

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