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International Conference on Graph Transformation

ICGT 2015: Graph Transformation pp 104–120Cite as

Reconfigurable Petri Nets with Transition Priorities and Inhibitor Arcs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9151))

Abstract

In this paper we introduce additional control structures for reconfigurable Petri nets. The main contributions are inhibitor arcs and transition priorities for reconfigurable Petri nets. The first ensure that a marking can inhibit the firing of a transition. Inhibitor arcs allow a transition to fire only if the adjacent place is empty. Transition priorities are given by an order of transitions and restrict the firing as well. A transition may fire only if it has the highest priority of all enabled transitions. Both concepts are compatible with reconfigurable Petri nets. In this paper we prove that place/transitions nets with inhibitor arcs and with transition priorities yield \(\mathcal {M}\)-adhesive categories. Hence, we obtain the well-known results for \(\mathcal {M}\)-adhesive categories. Moreover, we state the extension of our results to other types of Petri nets.

We illustrate the new concepts within an ongoing case study concerning travel agencies. This study deals with the organisation of processes that are constantly suspended by others. The main focus of the case study is to investigate the possibilities of small and medium travel agencies to provide a continuous service for their customers while travelling.

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Notes

  1. 1.

    See page 2 in [9] for the relation to other types of HLR systems.

  2. 2.

    For a discussion of the various adhesive categories see page 6 in [9].

  3. 3.

    In [25] they are called AHL-systems with morphisms that are isomorphisms on the algebra part.

  4. 4.

    For example, let \(P_0=\{0,5\}\) and \(P_1= \{0,3,5\}\) with f the inclusion and \(P_2=\{\bullet \}\), then \(3 \le _1 5\) yields \(([3],[\bullet ]) \in R_3\) and \(0 \le _1 3\) yields \(([\bullet ],[3]) \in R_3\), but \([\bullet ]=\{0,5\} \ne \{3\}=[3]\).

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Authors and Affiliations

  1. Hamburg University of Applied Sciences, Hamburg, Germany

    Julia Padberg

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  1. Julia Padberg
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Correspondence to Julia Padberg .

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Editors and Affiliations

  1. Dipartimento di Informatica, Sapienza Università di Roma, Rome, Italy

    Francesco Parisi-Presicce

  2. Angewandte Informatik 1, Universität Bayreuth, Bayreuth, Germany

    Bernhard Westfechtel

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Padberg, J. (2015). Reconfigurable Petri Nets with Transition Priorities and Inhibitor Arcs. In: Parisi-Presicce, F., Westfechtel, B. (eds) Graph Transformation. ICGT 2015. Lecture Notes in Computer Science(), vol 9151. Springer, Cham. https://doi.org/10.1007/978-3-319-21145-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-21145-9_7

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  • Online ISBN: 978-3-319-21145-9

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