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The Ideal View on Rackoff’s Coverability Technique

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Reachability Problems (RP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9328))

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Abstract

Rackoff’s small witness property for the coverability problem is the standard means to prove tight upper bounds in vector addition systems (VAS) and many extensions. We show how to derive the same bounds directly on the computations of the VAS instantiation of the generic backward coverability algorithm. This relies on a dual view of the algorithm using ideal decompositions of downwards-closed sets, which exhibits a key structural invariant in the VAS case. The same reasoning readily generalises to several VAS extensions.

Work funded in part by the Leverhulme Trust Visiting Professorship VP1-2014-041, and the EPSRC grant EP/M011801/1.

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Authors and Affiliations

  1. DIMAP, Department of Computer Science, University of Warwick, Coventry, UK

    Ranko Lazić & Sylvain Schmitz

  2. LSV, ENS Cachan and CNRS and INRIA, Cachan, France

    Sylvain Schmitz

Authors
  1. Ranko Lazić
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  2. Sylvain Schmitz
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Corresponding author

Correspondence to Sylvain Schmitz .

Editor information

Editors and Affiliations

  1. The Institute of Informatics, University of Warsaw, Warsaw, Poland

    Mikolai Bojanczyk

  2. The Institute of Informatics, University of Warsaw, Warsaw, Poland

    Slawomir Lasota

  3. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

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Lazić, R., Schmitz, S. (2015). The Ideal View on Rackoff’s Coverability Technique. In: Bojanczyk, M., Lasota, S., Potapov, I. (eds) Reachability Problems. RP 2015. Lecture Notes in Computer Science(), vol 9328. Springer, Cham. https://doi.org/10.1007/978-3-319-24537-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-24537-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24536-2

  • Online ISBN: 978-3-319-24537-9

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