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Compositions of (max, +) automata

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Abstract

This paper presents a compositional modeling approach by means of (max, +) automata. The motivation is to be able to model a complex discrete event system by composing sub-models representing its elementary parts. A direct modeling of safe timed Petri nets using (max, +) automata is first introduced. Based on this result, two types of synchronous product of (max, +) automata are proposed to model safe timed Petri nets obtained by merging places and/or transitions in subnets. An asynchronous product is finally proposed to represent particular bounded timed Petri nets.

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Notes

  1. The marking of any place is bounded by 1.

  2. This assumption is without loss of generality since an automaton with initial delays can always be transformed into an equivalent automaton with null initial delays by adding new states and by considering these delays as state transitions durations associated to new fictive initial events.

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Acknowledgments

Fruitful discussion with Philippe Darondeau (INRIA Rennes) is gratefully acknowledged. The authors thank the anonymous referees for their helpful comments.

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Authors and Affiliations

  1. LUNAM Université, LISA, Angers, France

    Sébastien Lahaye & Jean-Louis Boimond

  2. Institute of Mathematics - Brno Branch, Czech Academy of Sciences, Prague, Czech Republic

    Jan Komenda

Authors
  1. Sébastien Lahaye
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  2. Jan Komenda
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  3. Jean-Louis Boimond
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Corresponding author

Correspondence to Sébastien Lahaye.

Additional information

The previous version of this work was presented at WODES 2012, Guadalajara, Mexico (Lahaye et al. 2012a).

Research supported by the GAČR grants no. P103/11/0517 and by RVO: 67985840.

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Lahaye, S., Komenda, J. & Boimond, JL. Compositions of (max, +) automata. Discrete Event Dyn Syst 25, 323–344 (2015). https://doi.org/10.1007/s10626-014-0186-6

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  • DOI: https://doi.org/10.1007/s10626-014-0186-6

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