Petri Net Synthesis for Restricted Classes of Nets

  • Uli SchlachterEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9698)


This paper first recapitulates an algorithm for Petri net synthesis. Then, this algorithm is extended to special classes of Petri nets. For this purpose, any combination of the properties plain, pure, conflict-free, homogeneous, k-bounded, generalized T-net, generalized marked graph, place-output-nonbranching and distributed can be specified. Finally, a fast heuristic and an algorithm for minimizing the number of places in the synthesized Petri net is presented and evaluated experimentally.


Petri net synthesis Petri net properties Region theory Petri net minimization 



I would like to thank Harro Wimmel and Eike Best for their helpful comments. Special thanks go to Valentin Spreckels for the incorporation of homogeneity. Also, I am grateful for the anonymous reviewers’ careful reading and valuable comments.


  1. 1.
    Badouel, E., Bernardinello, L., Darondeau, P.: Polynomial algorithms for the synthesis of bounded nets. In: Mosses, P.D., Nielsen, M., Schwartzbach, M.I. (eds.) TAPSOFT 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995)Google Scholar
  2. 2.
    Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. Springer, Heidelberg (2015). Scholar
  3. 3.
    Badouel, E., Caillaud, B., Darondeau, P.: Distributing finite automata through Petri Net synthesis. Formal Asp. Comput. 13(6), 447–470 (2002). Scholar
  4. 4.
    Badouel, E., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) Lectures on Petri Nets I: Basic Models, Advances in Petri Nets, the Volumes are Based on the Advanced Course on Petri Nets, vol. 1491, pp. 529–586. Springer, Heidelberg (1996). Scholar
  5. 5.
    Barrett, C., Stump, A., Tinelli, C.: The SMT-LIB Standard: Version 2.0. In: Gupta, A., Kroening, D. (eds.) Proceedings of the 8th International Workshop on Satisfiability Modulo Theories, Edinburgh, UK (2010)Google Scholar
  6. 6.
    Best, E., Darondeau, P.: Petri Net distributability. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds.) PSI 2011. LNCS, vol. 7162, pp. 1–18. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    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, Heidelberg (2014)CrossRefGoogle Scholar
  8. 8.
    Best, E., Devillers, R.R.: State space axioms for t-systems. Acta Informatica 52(2–3), 133–152 (2015). Scholar
  9. 9.
    Best, E., Devillers, R.R.: Synthesis of bounded choice-free Petri Nets. In: Aceto, L., de Frutos-Escrig, D. (eds.) 26th International Conference on Concurrency Theory, CONCUR 2015, Madrid, Spain, September 1–4, 2015. LIPIcs, vol. 42, pp. 128–141. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2015).
  10. 10.
    Best, E., Schlachter, U.: Analysis of Petri Nets and transition systems. In: Knight, S., Lanese, I., Lluch-Lafuente, A., Vieira, H.T. (eds.) Proceedings 8th Interaction and Concurrency Experience, ICE 2015, Grenoble, France, 4–5 June 2015. EPTCS, vol. 189, pp. 53–67 (2015).
  11. 11.
    Borde, D., Dierkes, S., Ferrari, R., Gieseking, M., Göbel, V., Grunwald, R., von der Linde, B., Lückehe, D., Schlachter, U., Schierholz, C., Schwammberger, M., Spreckels, V.: APT: analysis of Petri nets and labeled transition systems.
  12. 12.
    Cabasino, M.P., Giua, A., Seatzu, C.: Identification of Petri Nets from knowledge of their language. Discrete Event Dyn. Syst. 17(4), 447–474 (2007). Scholar
  13. 13.
    Caillaud, B.: Synet: a synthesizer of distributable bounded Petri-nets from finite automata.
  14. 14.
    Carmona, J.: GENET: GEneralised NET synthesis.
  15. 15.
    Carmona, J.A., Cortadella, J., Kishinevsky, M.: A region-based algorithm for discovering Petri Nets from event logs. In: Dumas, M., Reichert, M., Shan, M.-C. (eds.) BPM 2008. LNCS, vol. 5240, pp. 358–373. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Carmona, J., Cortadella, J., Kishinevsky, M.: New region-based algorithms for deriving bounded petri nets. IEEE Trans. Comput. 59(3), 371–384 (2010). Scholar
  17. 17.
    Carmona, J., Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: A symbolic algorithm for the synthesis of bounded petri nets. In: van Hee and Valk [27], pp. 92–111.
  18. 18.
    Christ, J., Hoenicke, J., Nutz, A.: Proof tree preserving interpolation. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013 (ETAPS 2013). LNCS, vol. 7795, pp. 124–138. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  19. 19.
    Cortadella, J., Kishinevsky, M., Kondratyev, A., Lavagno, L., Yakovlev, A.: Petrify: a tool for manipulating concurrent specifications and synthesis of asynchronous controllers (1996)Google Scholar
  20. 20.
    Cortadella, J., Kishinevsky, M., Lavagno, L., Yakovlev, A.: Synthesizing petri nets from state-based models. In: Rudell, R.L. (ed.) Proceedings of the 1995 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1995, San Jose, California, USA, November 5–9, 1995, pp. 164–171. IEEE Computer Society/ACM (1995).
  21. 21.
    Cortadella, J., Kishinevsky, M., Lavagno, L., Yakovlev, A.: Deriving petri nets for finite transition systems. IEEE Trans. Computers 47(8), 859–882 (1998). Scholar
  22. 22.
    Cortadella, J., et al.: Petrify: a tool for synthesis of Petri nets and asynchronous circuits.
  23. 23.
    Darondeau, P.: Deriving unbounded Petri Nets from formal languages. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 533–548. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  24. 24.
    Dijkstra, E.W.: Hierarchical ordering of sequential processes. Acta Informatica 1, 115–138 (1971). Scholar
  25. 25.
    Ehrenfeucht, A., Rozenberg, G.: Partial (set) 2-structures. Part I: basic notions and the representation problem. Acta Informatica 27(4), 315–342 (1990). Scholar
  26. 26.
    Ehrenfeucht, A., Rozenberg, G.: Partial (set) 2-structures. Part II: state spaces of concurrent systems. Acta Inf 27(4), 343–368 (1990)CrossRefGoogle Scholar
  27. 27.
    van Hee, K.M., Valk, R. (eds.): Applications and Theory of Petri Nets, 29th International Conference, PETRI NETS 2008, Xi’an, China, 23–27, June 2008. Lecture Notes in Computer Science, vol. 5062 Springer (2008)Google Scholar
  28. 28.
    Lorenz, R., Mauser, S., Juhás, G.: How to synthesize nets from languages: a survey. In: Henderson, S.G., Biller, B., Hsieh, M., Shortle, J., Tew, J.D., Barton, R.R. (eds.) Proceedings of the Winter Simulation Conference, WSC 2007, Washington, DC, USA, December 9–12, 2007, pp. 637–647. WSC (2007).
  29. 29.
    van der Werf, J.M.E.M., van Dongen, B.F., Hurkens, C.A.J., Serebrenik, A.: Process discovery using integer linear programming. In: van Hee and Valk [27], pp. 368–387.

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Authors and Affiliations

  1. 1.Department of Computing ScienceCarl von Ossietzky UniversitätOldenburgGermany

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