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Eliminating Recursion in the μ-Calculus

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STACS 99 (STACS 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1563))

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Abstract

Consider the following problem: given a formula of the modal μ-calculus, decide whether this formula is equivalently expressible in basic modal logic. It is shown that this problem is decidable, in fact in deterministic exponential time. The decidability result can be obtained through a model theoretic reduction to the monadic second-order theory of the complete binary tree, which by Rabin’s classical result is decidable, albeit of non-elementary complexity. An improved analysis based on tree automata yields an exponential time decision procedure.

This is an extension of the original submission; the Exptime result, based on an automata theoretic analysis, is new here. Moreover, the original model theoretic approach has been simplified. I am very grateful to Moshe Vardi for having, with his comments on an earlier version, inspired these improvements.

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Author information

Authors and Affiliations

  1. RWTH Aachen, Germany

    Martin Otto

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  1. Martin Otto
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Editor information

Editors and Affiliations

  1. FB IV - Informatik, Universität Trier, D-54286, Trier, Germany

    Christoph Meinel

  2. LIFL, Université de Lille I, Bătiment 3, F-59655, Villeneuve d’Ascq Cedex, France

    Sophie Tison

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© 1999 Springer-Verlag Berlin Heidelberg

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Otto, M. (1999). Eliminating Recursion in the μ-Calculus. In: Meinel, C., Tison, S. (eds) STACS 99. STACS 1999. Lecture Notes in Computer Science, vol 1563. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49116-3_50

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  • DOI: https://doi.org/10.1007/3-540-49116-3_50

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65691-3

  • Online ISBN: 978-3-540-49116-3

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