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Firing Partial Orders in a Petri Net

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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

Petri nets have the simple firing rule that a transition is enabled to fire if its preset of places is marked. The occurrence of a transition is called an event. To check whether a sequence of events is enabled, we simply try to fire the sequence from ‘start’ to ‘end’ in the initial marking of the net. It is a bit of a stretch to call this an algorithm, but its runtime complexity is in \(O(|P| \cdot |V|)\), where P is the set of places and V is the set of events.

Petri nets model distributed systems. An execution of a distributed system is a partial order of events rather than a sequence. Compact tokenflows are tailored to an efficient algorithm that decides if a partial order of events is enabled in a Petri net. Yet, the runtime complexity of this algorithm is in \(O(|P| \cdot |V|^3)\).

In practical applications dealing with a huge amount of behavioral data, the gap between just firing a sequence and deciding if a partial order is enabled, makes a big difference.

In this paper, we present an approach to just firing a partial order of events in a Petri net. By firing a partial order, we obtain a lot of information about whether or not the partial order is enabled. We show that just firing is often enough if done correctly.

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Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, FernUniversität in Hagen, Hagen, Germany

    Robin Bergenthum

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  1. Robin Bergenthum
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Correspondence to Robin Bergenthum .

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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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Bergenthum, R. (2021). Firing Partial Orders in a Petri Net. 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_20

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-76982-6

  • Online ISBN: 978-3-030-76983-3

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