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A Framework for Classical Petri Net Problems: Conservative Petri Nets as an Application

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8489))

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Abstract

We present a framework based on permutations of firing sequences and on canonical firing sequences to approach computational problems involving classes of Petri nets with arbitrary arc multiplicities. As an example of application, we use these techniques to obtain PSPACE-completeness for the reachability and the covering problems of conservative Petri nets, generalizing known results for ordinary 1-conservative Petri nets. We also prove PSPACE-completeness for the RecLFS and the liveness problems of conservative Petri nets, for which, in case of ordinary 1-conservative Petri nets, PSPACE-membership but no matching lower bound has been known. Last, we show PSPACE-completeness for the containment and equivalence problems of conservative Petri nets. PSPACE-hardness of the problems mentioned above still holds if they are restricted to ordinary 1-conservative Petri nets.

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Authors and Affiliations

  1. Technische Universität München, 85748, Garching, Germany

    Ernst W. Mayr & Jeremias Weihmann

Authors
  1. Ernst W. Mayr
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  2. Jeremias Weihmann
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Editors and Affiliations

  1. Department of Computer Science, Iowa State University, 226 Atanasoff Hall, 50011, Ames, IA, USA

    Gianfranco Ciardo

  2. DTU Compute, Technical University of Denmark, Richard Pedersens Plads, 2800 Kgs., Lyngby, Denmark

    Ekkart Kindler

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Mayr, E.W., Weihmann, J. (2014). A Framework for Classical Petri Net Problems: Conservative Petri Nets as an Application. In: Ciardo, G., Kindler, E. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2014. Lecture Notes in Computer Science, vol 8489. Springer, Cham. https://doi.org/10.1007/978-3-319-07734-5_17

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  • DOI: https://doi.org/10.1007/978-3-319-07734-5_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07733-8

  • Online ISBN: 978-3-319-07734-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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