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Taking Complete Finite Prefixes to High Level, Symbolically

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2023)

Abstract

Unfoldings are a well known partial-order semantics of P/T Petri nets that can be applied to various model checking or verification problems. For high-level Petri nets, the so-called symbolic unfolding generalizes this notion. A complete finite prefix of the unfolding of a P/T Petri net contains all information to verify, e.g., reachability of markings. We unite these two concepts and define complete finite prefixes of the symbolic unfolding of high-level Petri nets. For a class of safe high-level Petri nets, we generalize the well-known algorithm by Esparza et al. for constructing small such prefixes. Additionally, we identify a more general class of nets with infinitely many reachable markings, for which an approach with an adapted cut-off criterion extends the complete prefix methodology, in the sense that the original algorithm cannot be applied to the P/T net represented by a high-level net.

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Notes

  1. 1.

    In the literature, the represented Petri net is often called the unfolding of the high-level Petri net. To avoid a clash of notions, we use the term expansion as, e.g., in [4].

  2. 2.

    The structure of this example is taken from Figure D.4.5 in [2].

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Würdemann, N., Chatain, T., Haar, S. (2023). Taking Complete Finite Prefixes to High Level, Symbolically. In: Gomes, L., Lorenz, R. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. Lecture Notes in Computer Science, vol 13929. Springer, Cham. https://doi.org/10.1007/978-3-031-33620-1_7

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  • DOI: https://doi.org/10.1007/978-3-031-33620-1_7

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