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On Functions Weakly Computable by Petri Nets and Vector Addition Systems

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Book cover Reachability Problems (RP 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8762))

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Abstract

We show that any unbounded function weakly computable by a Petri net or a VASS cannot be sublinear. This answers a long-standing folklore conjecture about weakly computing the inverses of some fast-growing functions. The proof relies on a pumping lemma for sets of runs in Petri nets or VASSes.

Work supported by the ReacHard project, ANR grant 11-BS02-001-01.

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Author information

Authors and Affiliations

  1. LaBRI, Univ. Bordeaux & CNRS, France

    J. Leroux

  2. LSV, ENS Cachan & CNRS, France

    Ph. Schnoebelen

Authors
  1. J. Leroux
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  2. Ph. Schnoebelen
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK

    Joël Ouaknine

  2. Department of Computer Science, University of Liverpool, Liverpool, UK

    Igor Potapov

  3. Department of Computer Science, University of Oxford, UK

    James Worrell

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Leroux, J., Schnoebelen, P. (2014). On Functions Weakly Computable by Petri Nets and Vector Addition Systems. In: Ouaknine, J., Potapov, I., Worrell, J. (eds) Reachability Problems. RP 2014. Lecture Notes in Computer Science, vol 8762. Springer, Cham. https://doi.org/10.1007/978-3-319-11439-2_15

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  • DOI: https://doi.org/10.1007/978-3-319-11439-2_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11438-5

  • Online ISBN: 978-3-319-11439-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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