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Reduction Using Induced Subnets to Systematically Prove Properties for Free-Choice 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

We use sequences of t-induced T-nets and p-induced P-nets to convert free-choice nets into T-nets and P-nets while preserving properties such as well-formedness, liveness, lucency, pc-safety, and perpetuality. The approach is general and can be applied to different properties. This allows for more systematic proofs that “peel off” non-trivial parts while retaining the essence of the problem (e.g., lifting properties from T-net and P-net to free-choice nets).

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Notes

  1. 1.

    \(\bigcup Q = \bigcup _{X \in Q} X\) for some set of sets Q.

  2. 2.

    The notions of T-reduction and P-reduction are unrelated to the “Desel rules” for free-choice nets without frozen tokens [8]. We allow for “bigger steps” and can reduce nets with frozen tokens (i.e., there may be an infinite firing sequence starting from a strictly smaller marking).

  3. 3.

    Note that \(\bullet {t_r}=\{p \mid (p,t_r) \in F^i\}\) depends on the net considered (here \(N^i\)).

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Authors and Affiliations

  1. Process and Data Science (Informatik 9), RWTH Aachen University, Aachen, Germany

    Wil M. P. van der Aalst

  2. Fraunhofer-Institut für Angewandte Informationstechnik (FIT), Sankt Augustin, Germany

    Wil M. P. van der Aalst

Authors
  1. Wil M. P. van der Aalst
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Correspondence to Wil M. P. van der Aalst .

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Editors and Affiliations

  1. Université de Genève, Carouge, Switzerland

    Didier Buchs

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep Carmona

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van der Aalst, W.M.P. (2021). Reduction Using Induced Subnets to Systematically Prove Properties for Free-Choice 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_11

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_11

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  • Print ISBN: 978-3-030-76982-6

  • Online ISBN: 978-3-030-76983-3

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