Simplifying the modal mu-calculus alternation hierarchy

  • J. C. Bradfield
Logic I
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1373)


In [Bra96], the strictness of the modal mu-calculus alternation hierarchy was shown by transferring a hierarchy from arithmetic; the latter was a corollary of a deep and highly technical analysis of [Lub93]. In this paper, we show that the alternation hierarchy in arithmetic can be established by entirely elementary means; further, simple examples of strict alternation depth n formulae can be constructed, which in turn give very simple examples to separate the modal hierarchy. In addition, the winning strategy formulae of parity games are shown to be such examples.


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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • J. C. Bradfield
    • 1
  1. 1.Department of Computer Science, University of EdinburghLaboratory for Foundations of Computer ScienceEdinburghUK

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