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Synchronizing sequences on a class of unbounded systems using synchronized Petri nets

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Abstract

Determining the state of a system when one does not know its current initial state is a very important problem in many practical applications as checking communication protocols, part orienteers, digital circuit reset, etc. Synchronizing sequences have been proposed in the 60’s to solve the problem on systems modeled by finite state machines. This paper presents a first investigation of the synchronizing problem on unbounded systems, using synchronized Petri nets, i.e., nets whose evolution is driven by external input events. The proposed approach suffers from the fact that no finite space representation can exhaustively answer to the reachability problem but we show that synchronizing sequences may be computed for a particular class of unbounded synchronized Petri nets.

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Notes

  1. Properly speaking, the model we describe here is called a place/transition net.

  2. Given two vectors \(x, y \in \mathbb {R}^{n}\) we write \(x \lneq y\) to denote that x ≤ y, i.e., each component of x is smaller than or equal to the corresponding component of y, and that x≠y, i.e., the two vectors are not identical.

  3. Here, * denotes the Kleene star operator and E ∗ represents the set of all sequences on alphabet E.

  4. We are assuming that target marking set can also include ω-markings.

  5. The completed graph is not shown in figure for sake of simplicity, but can be easily obtained adding selfloop labeled e|∅ as discussed in the previous subsection.

  6. Here M[w|σ j,w 〉 denotes that in the synchronized PN starting from marking M the input sequence w determines the firing of the step sequence σ j,w .

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Authors and Affiliations

  1. Aix Marseille Université, CNRS, ENSAM, Université de Toulon, LSIS UMR 7296, Marseille, 13397, France

    Marco Pocci, Isabel Demongodin, Norbert Giambiasi & Alessandro Giua

  2. DIEE, University of Cagliari, Cagliari, Italy

    Marco Pocci & Alessandro Giua

Authors
  1. Marco Pocci
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  2. Isabel Demongodin
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  3. Norbert Giambiasi
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  4. Alessandro Giua
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Correspondence to Isabel Demongodin.

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Pocci, M., Demongodin, I., Giambiasi, N. et al. Synchronizing sequences on a class of unbounded systems using synchronized Petri nets. Discrete Event Dyn Syst 26, 85–108 (2016). https://doi.org/10.1007/s10626-016-0225-6

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  • DOI: https://doi.org/10.1007/s10626-016-0225-6

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