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Decidable Classes of Unbounded Petri Nets with Time and Urgency

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9698))

Abstract

Adding real time information to Petri net models often leads to undecidability of classical verification problems such as reachability and boundedness. For instance, models such as Timed-Transition Petri nets (TPNs) [22] are intractable except in a bounded setting. On the other hand, the model of Timed-Arc Petri nets [26] enjoys decidability results for boundedness and control-state reachability problems at the cost of disallowing urgency (the ability to enforce actions within a time delay). Our goal is to investigate decidable classes of Petri nets with time that capture some urgency and still allow unbounded behaviors, which go beyond finite state systems.

We present, up to our knowledge, the first decidability results on reachability and boundedness for Petri net variants that combine unbounded places, time, and urgency. For this, we introduce the class of Timed-Arc Petri nets with restricted Urgency, where urgency can be used only on transitions consuming tokens from bounded places. We show that control-state reachability and boundedness are decidable for this new class, by extending results from Timed-Arc Petri nets (without urgency) [2]. Our main result concerns (marking) reachability, which is undecidable for both TPNs (because of unrestricted urgency) [20] and Timed-Arc Petri Nets (because of infinite number of “clocks”) [25]. We obtain decidability of reachability for unbounded TPNs with restricted urgency under a new, yet natural, timed-arc semantics presenting them as Timed-Arc Petri Nets with restricted urgency. Decidability of reachability under the intermediate marking semantics is also obtained for a restricted subclass.

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Acknowledgments

We thank the anonymous reviewers for their helpful suggestions which led to significant improvements in the presentation of this article. This work was partially supported by Indo-French CEFIPRA project AVERTS, by DST-INSPIRE faculty award [IFA12-MA-17], and by the DISTOL associated team of INRIA.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, IIT Bombay, Mumbai, India

    S. Akshay

  2. CNRS, IRISA, Rennes, France

    B. Genest

  3. INRIA, Campus de Beaulieu, Rennes, France

    L. Hélouët

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  1. S. Akshay
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  2. B. Genest
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  3. L. Hélouët
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Correspondence to S. Akshay .

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Editors and Affiliations

  1. Université Pierre and Marie Curie, Paris, France

    Fabrice Kordon

  2. Department Informatik, Universität Hamburg Department Informatik, Hamburg, Germany

    Daniel Moldt

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Akshay, S., Genest, B., Hélouët, L. (2016). Decidable Classes of Unbounded Petri Nets with Time and Urgency. In: Kordon, F., Moldt, D. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2016. Lecture Notes in Computer Science(), vol 9698. Springer, Cham. https://doi.org/10.1007/978-3-319-39086-4_18

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  • DOI: https://doi.org/10.1007/978-3-319-39086-4_18

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