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Branching Processes of Timed Petri Nets

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Perspectives of System Informatics (PSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9609))

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Abstract

The intention of this note is to spread the Couvreur et al.’s semantic framework of branching processes [9], suitable for describing the behavior of general Petri nets with interleaving semantics, to timed general Petri nets with step semantics in order to characterize unfolding as the greatest element of a complete lattice of branching processes. In case of maximal step semantics of timed Petri nets, we impose some restrictions on the model behavior and define a new class of branching processes and unfoldings under the name of apt ones which are shown to satisfy the complete lattice properties.

This work is supported in part by DFG-RFBR (project CAVER, grants BE 1267/14-1 and 14-01-91334).

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Notes

  1. 1.

    The number of arcs between each place and each transition is a natural number.

  2. 2.

    A marking contains a natural number of tokens in each net place.

  3. 3.

    The number of arcs between each place and each subset of transitions is a natural number.

References

  1. Aura, T., Lilius, J.: Time processes for time Petri nets. In: Azéma, P., Balbo, G. (eds.) ICATPN 1997. LNCS, vol. 1248, pp. 136–155. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  2. Baldan, P., Bruni, A., Corradini, A., Koenig, B., Rodriguez, C., Schwoon, S.: Efficient unfolding of contextual Petri nets. Theor. Comput. Sci. 449, 2–22 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  3. Baldan, P., Haar, S., König, B.: Distributed unfolding of Petri nets. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 126–141. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  4. Benveniste, A., Fabre, E., Jard, C., Haar, S.: Diagnosis of asynchronous discrete event systems, a net unfolding approach. IEEE Trans. Autom. Control 48(5), 714–727 (2003)

    Article  MathSciNet  Google Scholar 

  5. Bergenthum, R., Mauser, S., Lorenz, R., Juhas, G.: Unfolding semantics of Petri nets based on token flows. Fundamenta Informaticae 94(3–4), 331–360 (2009)

    MathSciNet  MATH  Google Scholar 

  6. Bonet, B., Haslum, P., Hickmott, S.L., Thiébaux, S.: Directed unfolding of Petri nets. In: Jensen, K., Aalst, W.M.P., Billington, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency I. LNCS, vol. 5100, pp. 172–198. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Bonet, B., Haslumb, P., Khomenko, V., Thiebauxb, S., Vogler, W.: Recent advances in unfolding technique. Theor. Comput. Sci. 551, 84–101 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chatain, T., Jard, C.: Time supervision of concurrent systems using symbolic unfoldings of time Petri nets. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 196–210. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Couvreur, J., Poitrenaud, D., Weil, P.: Branching processes of general Petri nets. Fundamenta Informaticae 122, 31–58 (2013)

    MathSciNet  MATH  Google Scholar 

  10. Engelfriet, J.: Branching processes of Petri nets. Acta Informatica 28(6), 575–591 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  11. Esparza, J.: Model checking using net unfoldings. Sci. Comput. Program. 23(2–3), 151–195 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. Fleischhack, H., Pelz, E.: Hierarchical timed high level nets and their branching processes. In: Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 397–416. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  13. Fleischhack, H., Stehno, C.: Computing a finite prefix of a time Petri net. In: Esparza, J., Lakos, C.A. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 163–181. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  14. Hickmott, S., Rintanen, J., Thiebaux, S., White, L.: Planning via Petri net unfolding. In: Proceedings of 20th International Joint Conference on Artificial Intelligence. AAAI Press, pp. 1904–1911(2007)

    Google Scholar 

  15. Khomenko, V., Koutny, M., Vogler, W.: Canonical prefixes of Petri net unfoldings. Acta Informatica 40(2), 95–118 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  16. Meseguer, J., Montanari, U., Sassone, V.: On the semantics of place/transition Petri nets. Math. Struct. Comput. Sci. 7(4), 359–397 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. Nielsen, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains. part i. theor. comput. sci. 13(1), 85–108 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  18. Popova-Zeugmann, L.: Time and Petri Nets, pp. 1–209. Springer, Heidelberg (2013). I-XI

    Book  MATH  Google Scholar 

  19. Valero, V., de Frutos, D., Cuartero, F.: Timed processes of timed Petri nets. In: DeMichelis, G., Díaz, M. (eds.) ICATPN 1995. LNCS, vol. 935, pp. 490–509. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. A.P. Ershov Institute of Informatics Systems, SB RAS, 6, Acad. Lavrentiev avenue, 630090, Novosibirsk, Russia

    Irina Virbitskaite & Victor Borovlyov

  2. Novosibirsk State University, 2, Pirogov avenue, 630090, Novosibirsk, Russia

    Irina Virbitskaite & Victor Borovlyov

  3. Humboldt University of Berlin, Unter den Linden 6, 10099, Berlin, Germany

    Louchka Popova-Zeugmann

Authors
  1. Irina Virbitskaite
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  2. Victor Borovlyov
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  3. Louchka Popova-Zeugmann
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Corresponding author

Correspondence to Irina Virbitskaite .

Editor information

Editors and Affiliations

  1. Innopolis University, Innopolis, Russia

    Manuel Mazzara

  2. The University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

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Virbitskaite, I., Borovlyov, V., Popova-Zeugmann, L. (2016). Branching Processes of Timed Petri Nets. In: Mazzara, M., Voronkov, A. (eds) Perspectives of System Informatics. PSI 2015. Lecture Notes in Computer Science(), vol 9609. Springer, Cham. https://doi.org/10.1007/978-3-319-41579-6_23

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  • DOI: https://doi.org/10.1007/978-3-319-41579-6_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-41578-9

  • Online ISBN: 978-3-319-41579-6

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