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On Flatness for 2-Dimensional Vector Addition Systems with States

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CONCUR 2004 - Concurrency Theory (CONCUR 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3170))

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Abstract

Vector addition systems with states (VASS) are counter automata where (1) counters hold nonnegative integer values, and (2) the allowed operations on counters are increment and decrement. Accelerated symbolic model checkers, like FAST, LASH or TReX, provide generic semi-algorithms to compute reachability sets for VASS (and for other models), but without any termination guarantee. Hopcroft and Pansiot proved that for 2-dim VASS (i.e. VASS with two counters), the reachability set is effectively semilinear. However, they use an ad-hoc algorithm that is specifically designed to analyze 2-dim VASS. In this paper, we show that 2-dim VASS are flat (i.e. they “intrinsically” contain no nested loops). We obtain that – forward, backward and binary – reachability sets are effectively semilinear for the class of 2-dim VASS, and that these sets can be computed using generic acceleration techniques.

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Author information

Authors and Affiliations

  1. DIRO, Université de Montréal, Montréal, QC, Canada

    Jérôme Leroux

  2. LaBRI, Univ. de Bordeaux & CNRS UMR, 5800, Talence, France

    Grégoire Sutre

Authors
  1. Jérôme Leroux
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  2. Grégoire Sutre
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Editor information

Editors and Affiliations

  1. Department of Computing, Imperial College London, 180 Queen’s Gate, SW7 2AZ, London, UK

    Philippa Gardner

  2. Department of Computing, Imperial College, London, UK

    Nobuko Yoshida

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Leroux, J., Sutre, G. (2004). On Flatness for 2-Dimensional Vector Addition Systems with States. In: Gardner, P., Yoshida, N. (eds) CONCUR 2004 - Concurrency Theory. CONCUR 2004. Lecture Notes in Computer Science, vol 3170. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28644-8_26

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  • DOI: https://doi.org/10.1007/978-3-540-28644-8_26

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22940-7

  • Online ISBN: 978-3-540-28644-8

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