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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.

References

  • Baccelli F, Cohen G, Olsder G-J, Quadrat J-P (1992) Synchronization and linearity. Wiley

  • Badouel E, Bouillard A, Darondeau P, Komenda J (2011) Residuation of tropical series: rationality issues. In: Joint 50th IEEE conference on decision and control and european control conference (CDC-ECC’11). pp 3855–3861

  • Buchholz P, Kemper P (2003) Weak bisimulation for (max/+) automata and related models. J Autom Lang Comb 8:187–218

    MATH  MathSciNet  Google Scholar 

  • Cassandras C G, Lafortune S (2006) Introduction to Des. Springer-Verlag, New York

    Google Scholar 

  • David R, Alla H (2010) Discrete, continuous, and hybrid Petri nets, 2nd edn. Springer, Paris

    Book  Google Scholar 

  • Gaubert S., Mairesse J. (1999) Asymptotic analysis of heaps of pieces and application to timed petri nets. In: Petri nets and performance models (PNPM’99). pp 158–169

  • Gaubert S, Mairesse J (1999) Modeling and analysis of timed petri nets using heaps of pieces. IEEE Trans Autom Control 44(4):683–698

    Article  MATH  MathSciNet  Google Scholar 

  • Gaubert S (1995) Performance Evaluation of (max, +) Automata. IEEE Trans Autom Control 40(12):2014–2025

    Article  MATH  MathSciNet  Google Scholar 

  • Houssin L (2011) Cyclic jobshop problem and (max,plus) algebra. In: 18th ifac world congress. Milan, pp 2717–2721

  • Kirsten D (2008) A burnside approach to the termination of mohri’s algorithm for polynomially ambiguous min-plus-automata. RAIRO - Theor Inf Appl 42(3):553–581

    Article  MATH  MathSciNet  Google Scholar 

  • Klimann I, Lombardy S, Mairesse J, Prieur C (2004) Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton. Theor Comput Sci:349–373

  • Komenda J, Lahaye S, Boimond J-L (2009) Le produit synchrone des automates (max, +). J Européen des Systèmes Automatisés 43(7)

  • Komenda J, Lahaye S, Boimond J-L (2009) Supervisory control of (max, +) automata: a behavioral approach. Discret Event Dyn Syst 19(4):525–549

    Article  MATH  MathSciNet  Google Scholar 

  • Lahaye S, Komenda J, Boimond J-L (2012) Compositions of (max, +) automata. In: International workshop on discrete event systems (WODES 2012). Guadalajara

  • Lahaye S, Komenda J, Boimond J-L (2012) Modélisation modulaire à l’aide d’automates (max, +). In: Conférence Internationale Francophone d’Automatique (CIFA’2012)

  • Lombardy S, Sakarovitch J (2006) Sequential?Theor Comput Sci 359(1–2):224–244

    Article  MathSciNet  Google Scholar 

  • Mairesse J, Vuillon L (2002) Asymptotic behavior in a heap model with two pieces. Theor Comput Sci 270(12):525–560

    Article  MATH  MathSciNet  Google Scholar 

  • Mohri M (2011) Weighted automata algorithms. In: Handbook of weighted automata. Springer

  • Murata T (1989) Petri nets: properties, analysis and applications. IEEE Proc Spec Issue Discret Event Syst 77:541–580

    Google Scholar 

  • Ramchandani C (1973) Analysis of asynchronous concurrent systems by timed Petri nets, PhD. Thesis, M.I.T.

  • Sakarovitch J (2003) Éléments de théorie des automates. Vuibert

  • Su R, van Schuppen JH, Rooda JE (2012) The synthesis of time optimal supervisors by using heaps-of-pieces. IEEE Trans Autom Control 57(1):105–118

    Article  Google Scholar 

Download references

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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