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International Workshop on Computer Science Logic

CSL 1999: Computer Science Logic pp 484–498Cite as

On Guarding Nested Fixpoints

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1683))

Abstract

For every hierarchicalsystem of equations S over some complete and distributive lattice we construct an equivalent system with the same set of variables which additionally is guarded. The price to be paid is that the resulting right-hand sides may grow exponentially. We therefore present methods how the exponentialbl ow-up can be avoided. Especially, the loop structure of the variable dependence graph is taken into account. Also we prove that size O(m· S) suffices whenever S originates from a fixpoint expression where the nesting-depth of fixpoints is at most m. Finally, we sketch an application to regular tree pattern-matching.

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Author information

Authors and Affiliations

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

    Helmut Seidl & Andreas Neumann

Authors
  1. Helmut Seidl
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  2. Andreas Neumann
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Editor information

Editors and Affiliations

  1. Mathematisches Institut, Universität Freiburg, Eckerstr. 1, D-79104, Freiburg, Germany

    Jörg Flum

  2. Dpto. de Sistemas Informáticos y Programación Edificio Fac. Matemáticas, Universidad Complutense de Madrid, Av. Complutense s/n, E-28040, Madrid, Spain

    Mario Rodriguez-Artalejo

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© 1999 Springer-Verlag Berlin Heidelberg

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Seidl, H., Neumann, A. (1999). On Guarding Nested Fixpoints. In: Flum, J., Rodriguez-Artalejo, M. (eds) Computer Science Logic. CSL 1999. Lecture Notes in Computer Science, vol 1683. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48168-0_34

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  • DOI: https://doi.org/10.1007/3-540-48168-0_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66536-6

  • Online ISBN: 978-3-540-48168-3

  • eBook Packages: Springer Book Archive

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