Flatness and Complexity of Immediate Observation Petri Nets

Authors Mikhail Raskin , Chana Weil-Kennedy , Javier Esparza

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Author Details

Mikhail Raskin
  • Technical University of Munich, Germany
Chana Weil-Kennedy
  • Technical University of Munich, Germany
Javier Esparza
  • Technical University of Munich, Germany


We thank Jérôme Leroux and Rupak Majumdar for interesting conversations that put us on the path of flatness and BIO nets. We also thank the reviewers whose comments allowed us to improve this paper, and fix a small mistake in Lemma 18.

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Mikhail Raskin, Chana Weil-Kennedy, and Javier Esparza. Flatness and Complexity of Immediate Observation Petri Nets. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 45:1-45:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


In a previous paper we introduced immediate observation (IO) Petri nets, a class of interest in the study of population protocols and enzymatic chemical networks. In the first part of this paper we show that IO nets are globally flat, and so their safety properties can be checked by efficient symbolic model checking tools using acceleration techniques, like FAST. In the second part we study Branching IO nets (BIO nets), whose transitions can create tokens. BIO nets extend both IO nets and communication-free nets, also called BPP nets, a widely studied class. We show that, while BIO nets are no longer globally flat, and their sets of reachable markings may be non-semilinear, they are still locally flat. As a consequence, the coverability and reachability problem for BIO nets, and even a certain set-parameterized version of them, are in PSPACE. This makes BIO nets the first natural net class with non-semilinear reachability relation for which the reachability problem is provably simpler than for general Petri nets.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed computing models
  • Theory of computation → Concurrency
  • Petri Nets
  • Reachability Analysis
  • Parameterized Verification
  • Flattability


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