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On Boundedness Problems for Pushdown Vector Addition Systems

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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

We study pushdown vector addition systems, which are synchronized products of pushdown automata with vector addition systems. The question of the boundedness of the reachability set for this model can be refined into two decision problems that ask if infinitely many counter values or stack configurations are reachable, respectively. Counter boundedness seems to be the more intricate problem. We show decidability in exponential time for one-dimensional systems. The proof is via a small witness property derived from an analysis of derivation trees of grammar-controlled vector addition systems.

This work was partially supported by ANR project ReacHard (ANR-11-BS02-001).

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Authors and Affiliations

  1. University of Bordeaux and CNRS, LaBRI, UMR 5800, Talence, France

    Jérôme Leroux & Grégoire Sutre

  2. Department of Computer Science, University of Warwick, Coventry, UK

    Patrick Totzke

Authors
  1. Jérôme Leroux
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  2. Grégoire Sutre
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  3. Patrick Totzke
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Corresponding author

Correspondence to Grégoire Sutre .

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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Leroux, J., Sutre, G., Totzke, P. (2015). On Boundedness Problems for Pushdown Vector Addition Systems. 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_10

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  • DOI: https://doi.org/10.1007/978-3-319-24537-9_10

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24536-2

  • Online ISBN: 978-3-319-24537-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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