Ambiguous Classes in the Games μ-Calculus Hierarchy

  • André Arnold
  • Luigi Santocanale
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2620)


Every parity game is a combinatorial representation of a closed Boolean μ-term. When interpreted in a distributive lattice every Boolean μ-term is equivalent to a fixed-point free term. The alternationdepth hierarchy is therefore trivial in this case. This is not the case for non distributive lattices, as the second author has shown that the alternation -depth hierarchy is infinite.

In this paper we show that the alternation-depth hierarchy of the games μ-calculus, with its interpretation in the class of all complete lattices, has a nice characterization of ambiguous classes: every parity game which is equivalent both to a game in σn+1 and to a game πn+1 is also equivalent to a game obtained by composing games in σn and πn.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • André Arnold
    • 1
  • Luigi Santocanale
    • 1
  1. 1.LaBRIUniversité Bordeaux 1Bordeaux

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