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Causality in Extensions of Petri Nets

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Transactions on Petri Nets and Other Models of Concurrency VII

Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 7480))

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Abstract

The causal semantics of standard net classes like Elementary Net Systems and Place/Transition Nets, is typically expressed in terms of partially ordered sets of transition occurrences. In each such partial order, causally related occurrences are ordered while concurrent transition occurrences remain unordered. Partial order semantics can, in particular, support model checking by efficient verification techniques based on net unfoldings.

To enhance the modelling power of standard net classes, one can introduce different forms of ‘testing’ using, for example, inhibitor arcs. However, the causal semantics of such extended nets can often no longer be described solely in terms of partial orders. In this paper, we explain what modifications to the partial order semantics are needed in order to provide a satisfactory treatment for nets with activator, inhibitor and mutex arcs. On the technical side, the proposed solution is based on causal structures which enrich partial orders with additional order relations corresponding to other aspects of causality. With en-systems as our starting point, we discuss how their extensions can be treated using these richer notions of causality.

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Author information

Authors and Affiliations

  1. LIACS, Leiden University, Leiden, 2300 RA, The Netherlands

    Jetty Kleijn

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, NE1 7RU, United Kingdom

    Maciej Koutny

Authors
  1. Jetty Kleijn
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  2. Maciej Koutny
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Editor information

Editors and Affiliations

  1. Faculty of Science, Department of Computer Science, University of Aarhus, IT-parken, Aabogade 34, 8200, Aarhus N, Denmark

    Kurt Jensen

  2. Department of Information Systems, Eindhoven University of Technology, P.O. Box 513, NL-5600, Eindhoven, MB, The Netherlands

    Wil M. P. van der Aalst

  3. Dipartimento di Informatica, Università degli Studi di Torino, Corso Svizzera 185, 10149, Torino, Italy

    Gianfranco Balbo

  4. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Maciej Koutny

  5. Institut für Informatik, Universität Rostock, Germany

    Karsten Wolf

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Kleijn, J., Koutny, M. (2013). Causality in Extensions of Petri Nets. In: Jensen, K., van der Aalst, W.M.P., Balbo, G., Koutny, M., Wolf, K. (eds) Transactions on Petri Nets and Other Models of Concurrency VII. Lecture Notes in Computer Science, vol 7480. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38143-0_6

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  • DOI: https://doi.org/10.1007/978-3-642-38143-0_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38142-3

  • Online ISBN: 978-3-642-38143-0

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