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On Liveness and Deadlockability in Subclasses of Weighted Petri Nets

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10258))

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Abstract

Structural approaches have greatly simplified the analysis of intractable properties in Petri nets, notably liveness. In this paper, we further develop these structural methods in particular weighted subclasses of Petri nets to analyze liveness and deadlockability, the latter property being a strong form of non-liveness.

For homogeneous join-free nets, from the analysis of specific substructures, we provide the first polynomial-time characterizations of structural liveness and structural deadlockability, expressing respectively the existence of a live marking and the deadlockability of every marking.

For the join-free class, assuming structural boundedness and leaving out the homogeneity constraint, we show that liveness is not monotonic, meaning not always preserved upon any increase of a live marking.

Finally, we use this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.

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Notes

  1. 1.

    Moreover, the well-known necessary conditions of liveness based on siphons containing traps or based on the existence of a repetitive vector [3, 5, 18] do not help.

  2. 2.

    In this paper, we study siphons that may contain traps, remarkably in JF nets. Hence, we cannot use the results of [3]. Also, our nets will often be structurally repetitive (weakly sur-consistent), which is another well-known necessary condition of structural liveness (Proposition 10 in [18]) that is not sufficient in the HJF class.

  3. 3.

    Each of them has traps and is weakly sur-consistent (i.e. structurally repetitive).

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Authors and Affiliations

  1. Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Thomas Hujsa

  2. Département d’Informatique, Université Libre de Bruxelles, Brussels, Belgium

    Raymond Devillers

Authors
  1. Thomas Hujsa
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  2. Raymond Devillers
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Correspondence to Thomas Hujsa .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science (MF 7.103), Eindhoven University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Wil van der Aalst

  2. Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Eike Best

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Hujsa, T., Devillers, R. (2017). On Liveness and Deadlockability in Subclasses of Weighted Petri Nets. In: van der Aalst, W., Best, E. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2017. Lecture Notes in Computer Science(), vol 10258. Springer, Cham. https://doi.org/10.1007/978-3-319-57861-3_16

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  • DOI: https://doi.org/10.1007/978-3-319-57861-3_16

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