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Petri Net Synthesis with Union/Find

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10877))

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Abstract

We propose a new algorithm for the synthesis of a Petri net from a transition system. It is presented for a class of place/transition Petri nets we call \(\varDelta \)1-Petri nets. A \(\varDelta \)1-Petri net has an incidence matrix where entries have values 0, 1, and −1 only. This class includes safe Petri nets as well as ordinary place/transition nets. The proposed algorithm can be adapted to these net classes. The algorithm employs Tarjan’s union/find algorithm for managing sets of vertices. It requires just O(|V||T|) space where V is the set of vertices and T is the set of transition labels. Consequently, problem instances even beyond 1,000,000 vertices have a manageable memory footprint. Our results are experimentally validated using a prototype implementation.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Rostock, Rostock, Germany

    Karsten Wolf

Authors
  1. Karsten Wolf
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Correspondence to Karsten Wolf .

Editor information

Editors and Affiliations

  1. University of Newcastle, Newcastle upon Tyne, United Kingdom

    Victor Khomenko

  2. École Centrale de Nantes, Nantes Cedex 3, France

    Olivier H. Roux

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Wolf, K. (2018). Petri Net Synthesis with Union/Find. In: Khomenko, V., Roux, O. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2018. Lecture Notes in Computer Science(), vol 10877. Springer, Cham. https://doi.org/10.1007/978-3-319-91268-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-91268-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-91267-7

  • Online ISBN: 978-3-319-91268-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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