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Hardness Results for the Synthesis of b-bounded Petri Nets

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11522))

Abstract

Synthesis for a type \(\tau \) of Petri nets is the following search problem: For a transition system A, find a Petri net N of type \(\tau \) whose state graph is isomorphic to A, if there is one. To determine the computational complexity of synthesis for types of bounded Petri nets we investigate their corresponding decision version, called feasibility. We show that feasibility is NP-complete for (pure) b-bounded P/T-nets if \(b\in \mathbb {N}^+\). We extend (pure) b-bounded P/T-nets by the additive group \(\mathbb {Z}_{b+1}\) of integers modulo \((b+1)\) and show feasibility to be NP-complete for the resulting type. To decide if A has the event state separation property is shown to be NP-complete for (pure) b-bounded and group extended (pure) b-bounded P/T-nets. Deciding if A has the state separation property is proven to be NP-complete for (pure) b-bounded P/T-nets.

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Acknowledgements

I would like to thank Christian Rosenke and Uli Schlachter for their precious remarks. Also, I’m thankful to the anonymous reviewers for their helpful comments.

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Authors and Affiliations

  1. Universität Rostock, Institut für Informatik, Theoretische Informatik, Albert-Einstein-Straße 22, 18059, Rostock, Germany

    Ronny Tredup

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  1. Ronny Tredup
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Correspondence to Ronny Tredup .

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Editors and Affiliations

  1. Università di Torino, Turin, Italy

    Susanna Donatelli

  2. Inria and LSV, CNRS & ENS Paris-Saclay, Cachan Cedex, France

    Stefan Haar

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Tredup, R. (2019). Hardness Results for the Synthesis of b-bounded Petri Nets. In: Donatelli, S., Haar, S. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2019. Lecture Notes in Computer Science(), vol 11522. Springer, Cham. https://doi.org/10.1007/978-3-030-21571-2_9

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  • DOI: https://doi.org/10.1007/978-3-030-21571-2_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-21570-5

  • Online ISBN: 978-3-030-21571-2

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