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Parameterized Analysis of Immediate Observation Petri Nets

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

Abstract

We introduce immediate observation Petri nets, a class of interest in the study of population protocols (a model of distributed computation), and enzymatic chemical networks. In these areas, relevant analysis questions translate into parameterized Petri net problems: whether an infinite set of Petri nets with the same underlying net, but different initial markings, satisfy a given property. We study the parameterized reachability, coverability, and liveness problems for immediate observation Petri nets. We show that all three problems are in \(\mathsf {PSPACE}\) for infinite sets of initial markings defined by counting constraints, a class sufficiently rich for the intended application. This is remarkable, since the problems are already \(\mathsf {PSPACE}\)-hard when the set of markings is a singleton, i.e., in the non-parameterized case. We use these results to prove that the correctness problem for immediate observation population protocols is \(\mathsf {PSPACE}\)-complete, answering a question left open in a previous paper.

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 787367 (PaVeS).

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Notes

  1. 1.

    The Petri nets of [4] are in fact slightly more general than IO nets, but equivalent to them for properties that depend only on the reachability graph, as are the net properties studied in [4].

  2. 2.

    Actually, our counting constraints correspond to the “counting constraints in normal form” of [14]. We shorten the name, because we never need counting constraints not in normal form.

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Acknowledgments

We thank three anonymous reviewers for numerous suggestions to improve readability, and Pierre Ganty for many helpful discussions.

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Correspondence to Chana Weil-Kennedy .

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Esparza, J., Raskin, M., Weil-Kennedy, C. (2019). Parameterized Analysis of Immediate Observation 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_20

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  • DOI: https://doi.org/10.1007/978-3-030-21571-2_20

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