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Computing Parameterized Invariants of Parameterized Petri Nets

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12734))

Abstract

A fundamental advantage of Petri net models is the possibility to automatically compute useful system invariants from the syntax of the net. Classical techniques used for this are place invariants, P-components, siphons or traps. Recently, Bozga et al. have presented a novel technique for the parameterized verification of safety properties of systems with a ring or array architecture. They show that the statement “for every instance of the parameterized Petri net, all markings satisfying the linear invariants associated to all the P-components, siphons and traps of the instance are safe” can be encoded in WS1S and checked using tools like MONA. However, while the technique certifies that this infinite set of linear invariants extracted from P-components, siphons or traps are strong enough to prove safety, it does not return an explanation of this fact understandable by humans. We present a CEGAR loop that constructs a finite set of parameterized P-components, siphons or traps, whose infinitely many instances are strong enough to prove safety. For this we design parameterization procedures for different architectures.

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Notes

  1. 1.

    The CEGAR loop for the non-parametric case could be formulated in SAT and solved using a SAT-solver. However, we formulate it in WS1S, since this allows us to give a uniform description of the non-parametric and the parametric cases.

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Authors and Affiliations

  1. Technical University of Munich, Munich, Germany

    Javier Esparza, Mikhail Raskin & Christoph Welzel

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  1. Javier Esparza
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  2. Mikhail Raskin
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  3. Christoph Welzel
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Correspondence to Christoph Welzel .

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  1. Université de Genève, Carouge, Switzerland

    Didier Buchs

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep Carmona

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Esparza, J., Raskin, M., Welzel, C. (2021). Computing Parameterized Invariants of Parameterized Petri Nets. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_8

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_8

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