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Analysis and Synthesis of Weighted Marked Graph Petri Nets

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10877))

Abstract

Numerous real-world systems can be modeled with Petri nets, which allow a combination of concurrency with synchronizations and conflicts. To alleviate the difficulty of checking their behaviour, a common approach consists in studying specific subclasses. In the converse problem of Petri net synthesis, a Petri net of some subclass has to be constructed efficiently from a given specification, typically from a labelled transition system describing the behaviour of the desired net.

In this paper, we focus on a notorious subclass of persistent Petri nets, the weighted marked graphs (WMGs), also called generalised (or weighted) event (or marked) graphs or weighted T-nets. In such nets, edges have multiplicities (weights) and each place has at most one ingoing and one outgoing transition. Although extensively studied in previous works and benefiting from strong results, both their analysis and synthesis can be further investigated. To this end, we provide new conditions delineating more precisely their behaviour and give a dedicated synthesis procedure.

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Notes

  1. 1.

    This is the only way to define an adequate \(p_{a,b}\); in particular, there is no \(p_{*,b}\) or \(p_{a,*}\).

References

  1. Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-47967-4

    Book  MATH  Google Scholar 

  2. Best, E., Devillers, R.: Characterisation of the state spaces of live and bounded marked graph Petri nets. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 161–172. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04921-2_13

    Chapter  MATH  Google Scholar 

  3. Best, E., Devillers, R.: Synthesis of persistent systems. In: Ciardo, G., Kindler, E. (eds.) PETRI NETS 2014. LNCS, vol. 8489, pp. 111–129. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-07734-5_7

    Chapter  MATH  Google Scholar 

  4. Best, E., Devillers, R.: State space axioms for T-systems. Acta Inf. 52(2–3), 133–152 (2015). https://doi.org/10.1007/s00236-015-0219-0

    Article  MathSciNet  MATH  Google Scholar 

  5. Best, E., Devillers, R.: Synthesis and reengineering of persistent systems. Acta Inf. 52(1), 35–60 (2015). https://doi.org/10.1007/s00236-014-0209-7

    Article  MathSciNet  MATH  Google Scholar 

  6. Best, E., Devillers, R.: Synthesis of bounded choice-free Petri nets. In: Aceto, L., Frutos Escrig, D. (eds.) Proceedings of 26th International Conference on Concurrency Theory (CONCUR 2015), pp. 128–141 (2015). https://doi.org/10.4230/LIPIcs.CONCUR.2015.128

  7. Best, E., Devillers, R.: Synthesis of live and bounded persistent systems. Fundam. Inform. 140, 39–59 (2015). https://doi.org/10.3233/FI-2015-1244

    Article  MathSciNet  MATH  Google Scholar 

  8. Best, E., Devillers, R.: Characterisation of the state spaces of marked graph Petri nets. Inf. Comput. 253(3), 399–410 (2017). https://doi.org/10.1016/j.ic.2016.06.006

    Article  MathSciNet  MATH  Google Scholar 

  9. Best, E., Devillers, R., Schlachter, U.: Bounded choice-free Petri net synthesis: algorithmic issues. Acta Inform. 54, 1–37 (2017)

    Article  MathSciNet  Google Scholar 

  10. Commoner, F., Holt, A., Even, S., Pnueli, A.: Marked directed graphs. J. Comput. Syst. Sci. 5(5), 511–523 (1971). https://doi.org/10.1016/S0022-0000(71)80013-2

    Article  MathSciNet  MATH  Google Scholar 

  11. Crespi-Reghizzi, S., Mandrioli, D.: A decidability theorem for a class of vector-addition systems. Inf. Process. Lett. 3(3), 78–80 (1975). https://doi.org/10.1016/0020-0190(75)90020-4

    Article  MathSciNet  MATH  Google Scholar 

  12. Darondeau, P.: Equality of languages coincides with isomorphism of reachable state graphs for bounded and persistent Petri nets. Inf. Process. Lett. 94(6), 241–245 (2005). https://doi.org/10.1016/j.ipl.2005.03.002

    Article  MathSciNet  MATH  Google Scholar 

  13. Desel, J., Esparza, J.: Free Choice Petri Nets, Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, New York (1995)

    Book  Google Scholar 

  14. Devillers, R.: Products of transition systems and additions of Petri nets. In: Desel, J., Yakovlev, A. (eds.) Proceedings of 16th International Conference on Application of Concurrency to System Design (ACSD 2016), pp. 65–73 (2016). https://doi.org/10.1109/ACSD.2016.10

  15. Devillers, R.: Factorisation of transition systems. Acta Inform. 54, 1–24 (2017). https://doi.org/10.1007/s00236-017-0300-y

    Article  MathSciNet  Google Scholar 

  16. Devillers, R., Schlachter, U.: Factorisation of Petri net solvable transition systems. In: 39th International Conference on Applications and Theory of Petri Nets and Concurrency, Bratislava (2018)

    Google Scholar 

  17. Hujsa, T., Delosme, J.M., Munier-Kordon, A.: On liveness and reversibility of equal-conflict Petri nets. Fundam. Inform. 146(1), 83–119 (2016). https://doi.org/10.3233/FI-2016-1376

    Article  MathSciNet  MATH  Google Scholar 

  18. Hujsa, T., Devillers, R.: On liveness and deadlockability in subclasses of weighted Petri nets. In: van der Aalst, W., Best, E. (eds.) PETRI NETS 2017. LNCS, vol. 10258, pp. 267–287. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57861-3_16

    Chapter  Google Scholar 

  19. Keller, R.M.: A fundamental theorem of asynchronous parallel computation. In: Feng, T. (ed.) Parallel Processing. LNCS, vol. 24, pp. 102–112. Springer, Heidelberg (1975). https://doi.org/10.1007/3-540-07135-0_113

    Chapter  Google Scholar 

  20. Lee, E., Messerschmidt, D.: Static scheduling of synchronous data flow programs for digital signal processing. IEEE Trans. Comput. C–36(1), 24–35 (1987). https://doi.org/10.1109/TC.1987.5009446

    Article  MATH  Google Scholar 

  21. Lee, E.A., Messerschmitt, D.G.: Synchronous data flow. Proc. IEEE 75(9), 1235–1245 (1987)

    Article  Google Scholar 

  22. Marchetti, O., Munier-Kordon, A.: A sufficient condition for the liveness of weighted event graphs. Eur. J. Oper. Res. 197(2), 532–540 (2009). https://doi.org/10.1016/j.ejor.2008.07.037

    Article  MathSciNet  MATH  Google Scholar 

  23. Pino, J.L., Bhattacharyya, S.S., Lee, E.A.: A hierarchical multiprocessor scheduling framework for synchronous dataflow graphs. Technical report, University of California, Berkeley, May 1995

    Google Scholar 

  24. Silva, M., Terue, E., Colom, J.M.: Linear algebraic and linear programming techniques for the analysis of place/transition net systems. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 309–373. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-65306-6_19

    Chapter  Google Scholar 

  25. Sriram, S., Bhattacharyya, S.S.: Embedded Multiprocessors: Scheduling and Synchronization. Signal Processing and Communications. CRC Press, Boca Raton (2009)

    Book  Google Scholar 

  26. Teruel, E., Chrzastowski-Wachtel, P., Colom, J.M., Silva, M.: On weighted T-systems. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 348–367. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55676-1_20

    Chapter  Google Scholar 

  27. Teruel, E., Colom, J.M., Silva, M.: Choice-free Petri nets: a model for deterministic concurrent systems with bulk services and arrivals. IEEE Trans. Syst. Man Cybern. Part A 27(1), 73–83 (1997). https://doi.org/10.1109/3468.553226

    Article  Google Scholar 

  28. Teruel, E., Silva, M.: Structure theory of equal conflict systems. Theor. Comput. Sci. 153(1–2), 271–300 (1996). https://doi.org/10.1016/0304-3975(95)00124-7

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Département d’Informatique, Université Libre de Bruxelles, 1050, Brussels, Belgium

    Raymond Devillers

  2. Department of Computing Science, Carl von Ossietzky Universität Oldenburg, 26111, Oldenburg, Germany

    Thomas Hujsa

Authors
  1. Raymond Devillers
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  2. Thomas Hujsa
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Correspondence to Thomas Hujsa .

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Editors and Affiliations

  1. University of Newcastle, Newcastle upon Tyne, United Kingdom

    Victor Khomenko

  2. École Centrale de Nantes, Nantes Cedex 3, France

    Olivier H. Roux

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Devillers, R., Hujsa, T. (2018). Analysis and Synthesis of Weighted Marked Graph Petri Nets. In: Khomenko, V., Roux, O. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2018. Lecture Notes in Computer Science(), vol 10877. Springer, Cham. https://doi.org/10.1007/978-3-319-91268-4_2

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  • DOI: https://doi.org/10.1007/978-3-319-91268-4_2

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  • Print ISBN: 978-3-319-91267-7

  • Online ISBN: 978-3-319-91268-4

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