A Symbolic Algorithm for the Synthesis of Bounded Petri Nets

  • J. Carmona
  • J. Cortadella
  • M. Kishinevsky
  • A. Kondratyev
  • L. Lavagno
  • A. Yakovlev
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5062)


This paper presents an algorithm for the synthesis of bounded Petri nets from transition systems. A bounded Petri net is always provided in case it exists. Otherwise, the events are split into several transitions to guarantee the synthesis of a Petri net with bisimilar behavior. The algorithm uses symbolic representations of multisets of states to efficiently generate all the minimal regions. The algorithm has been implemented in a tool. Experimental results show a significant net reduction when compared with approaches for the synthesis of safe Petri nets.


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  1. [BBD95]
    Badouel, E., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Schwartzbach, M.I., Nielsen, M. (eds.) CAAP 1995, FASE 1995, and TAPSOFT 1995. LNCS, vol. 915, pp. 364–383. Springer, Heidelberg (1995)Google Scholar
  2. [BD98]
    Badouel, E., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) Lectures on Petri Nets I: Basic Models. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998)Google Scholar
  3. [BDLS07]
    Bergenthum, R., Desel, J., Lorenz, R., Mauser, S.: Process mining based on regions of languages. In: Alonso, G., Dadam, P., Rosemann, M. (eds.) BPM 2007. LNCS, vol. 4714, pp. 375–383. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. [Bry86]
    Bryant, R.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computer-Aided Design 35(8), 677–691 (1986)MATHGoogle Scholar
  5. [Cai02]
    Caillaud, B.: Synet: A synthesizer of distributable bounded Petri-nets from finite automata (2002), http://www.irisa.fr/s4/tools/synet/
  6. [CGP00]
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. The MIT Press, Cambridge (2000)Google Scholar
  7. [CKLY98]
    Cortadella, J., Kishinevsky, M., Lavagno, L., Yakovlev, A.: Deriving Petri nets from finite transition systems. IEEE Transactions on Computers 47(8), 859–882 (1998)CrossRefMathSciNetGoogle Scholar
  8. [Dar07]
    Darondeau, P.: Synthesis and control of asynchronous and distributed systems. In: Basten, T., Juhás, G., Shukla, S.K. (eds.) ACSD. IEEE Computer Society, Los Alamitos (2007)Google Scholar
  9. [DR96]
    Desel, J., Reisig, W.: The synthesis problem of Petri nets. Acta Informatica 33(4), 297–315 (1996)CrossRefMathSciNetGoogle Scholar
  10. [ER90]
    Ehrenfeucht, A., Rozenberg, G.: Partial (Set) 2-Structures. Part I, II. Acta Informatica 27, 315–368 (1990)MATHMathSciNetCrossRefGoogle Scholar
  11. [HKT95]
    Hoogers, P.W., Kleijn, H.C.M., Thiagarajan, P.S.: A trace semantics for petri nets. Inf. Comput. 117(1), 98–114 (1995)MATHCrossRefMathSciNetGoogle Scholar
  12. [HKT96]
    Hoogers, P.W., Kleijn, H.C.M., Thiagarajan, P.S.: An event structure semantics for general petri nets. Theor. Comput. Sci. 153(1&2), 129–170 (1996)MATHCrossRefMathSciNetGoogle Scholar
  13. [Maz87]
    Mazurkiewicz, A.W.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 279–324. Springer, Heidelberg (1987)Google Scholar
  14. [Mil89]
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  15. [Muk92]
    Mukund, M.: Petri nets and step transition systems. Int. Journal of Foundations of Computer Science 3(4), 443–478 (1992)MATHCrossRefMathSciNetGoogle Scholar
  16. [SBY07]
    Sokolov, D., Bystrov, A., Yakovlev, A.: Direct mapping of low-latency asynchronous controllers from STGs. IEEE Transactions on Computer-Aided Design 26(6), 993–1009 (2007)CrossRefGoogle Scholar
  17. [VPWJ07]
    Verbeek, H.M.W., Pretorius, A.J., van der Aalst, W.M.P., van Wijk, J.J.: On Petri-net synthesis and attribute-based visualization. In: Proc. Workshop on Petri Nets and Software Engineering (PNSE 2007), pp. 127–141 (June 2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • J. Carmona
    • 1
  • J. Cortadella
    • 1
  • M. Kishinevsky
    • 2
  • A. Kondratyev
    • 3
  • L. Lavagno
    • 4
  • A. Yakovlev
    • 5
  1. 1.Universitat Politècnica de CatalunyaSpain
  2. 2.Intel CorporationUSA
  3. 3.Cadence Berkeley LaboratoriesUSA
  4. 4.Politecnico di TorinoItaly
  5. 5.Newcastle UniversityUK

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