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Interval Traces with Mutex Relation

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13929))

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Abstract

Interval traces can model sophisticated behaviours of concurrent systems under the assumptions that all observations/system runs are represented by interval orders and simultaneity is not necessarily transitive. What they cannot model is the case when a and b are considered independent, interleavings ab and ba are deemed equivalent, but simultaneous execution of a and b is disallowed. We introduce a new kind of interval traces, incorporating a mutex relation, that can model these kind of cases. We discuss the soundness of this concept and show how it can be applied in the domain of Petri nets.

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Notes

  1. 1.

    Mazurkiewicz traces do not forbid simultaneous executions of a and b for independent a and b, they just do not express it explicitly.

  2. 2.

    Defining interval step sequences is mathematically possible but it does not make much sense as \(t_\upharpoonright \) and \(t_\downharpoonright \) are interpreted as event beginning and its end, i.e., they are instantaneous, so their simultaneous occurrence is not observable - when time is continuous, or it can entirely be represented by interleaving - when time is discrete (see [22, 34]).

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Acknowledgment

A partial support by the Discovery NSERC of Canada grant No. 6466-15, and the Leverhulme Trust grant RPG-2022-025 is acknowledged. The authors gratefully acknowledge four anonymous referees, whose comments significantly contributed to the final version of this paper.

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Authors and Affiliations

  1. Department of Computing and Software, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Ryszard Janicki

  2. School of Computing, Newcastle University, Newcastle upon Tyne, NE4 5TG, UK

    Maciej Koutny

  3. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, 12/18, Poland

    Łukasz Mikulski

Authors
  1. Ryszard Janicki
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  2. Maciej Koutny
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Correspondence to Łukasz Mikulski .

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Editors and Affiliations

  1. NOVA University Lisbon, Caparica, Portugal

    Luis Gomes

  2. University of Augsburg, Augsburg, Germany

    Robert Lorenz

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Janicki, R., Koutny, M., Mikulski, Ł. (2023). Interval Traces with Mutex Relation. In: Gomes, L., Lorenz, R. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2023. Lecture Notes in Computer Science, vol 13929. Springer, Cham. https://doi.org/10.1007/978-3-031-33620-1_8

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