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Simplifying the modal mu-calculus alternation hierarchy

  • Logic I
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

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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Authors and Affiliations

  1. Department of Computer Science, University of Edinburgh, Laboratory for Foundations of Computer Science, EH9 3JZ, Edinburgh, UK

    J. C. Bradfield

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  1. J. C. Bradfield
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Bradfield, J.C. (1998). Simplifying the modal mu-calculus alternation hierarchy. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028547

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  • DOI: https://doi.org/10.1007/BFb0028547

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

  • eBook Packages: Springer Book Archive

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