Over-Approximative Petri Net Synthesis for Restricted Subclasses of Nets

  • Uli Schlachter
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10792)


We show that, given a finite lts, there is a minimal bounded Petri net over-approximation according to a structural preorder and present an algorithm to compute this over-approximation. This result is extended to subclasses of nets, namely pure Petri nets, plain Petri nets, T-nets, and marked graphs, plus combinations of these properties.


Petri net synthesis Petri net properties Region theory 



The author would like to thank the anonymous reviewers, Eike Best, and Harro Wimmel for their very useful 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.) CAAP 1995. LNCS, vol. 915, pp. 364–378. Springer, Heidelberg (1995). CrossRefGoogle Scholar
  2. 2.
    Badouel, E., Bernardinello, L., Darondeau, P.: Petri Net Synthesis. TTCS. Springer, Heidelberg (2015). CrossRefzbMATHGoogle Scholar
  3. 3.
    Badouel, E., Darondeau, P.: Theory of regions. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 529–586. Springer, Heidelberg (1998). CrossRefGoogle Scholar
  4. 4.
    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). CrossRefGoogle Scholar
  5. 5.
    Best, E., Devillers, R.: State space axioms for T-systems. Acta Inf. 52(2–3), 133–152 (2015). MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Carmona, J., 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
  7. 7.
    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
  8. 8.
    Ehrenfeucht, A., Rozenberg, G.: Partial (set) 2-structures. Part I: basic notions and the representation problem and Part II: state spaces of concurrent systems. Acta Inf. 27(4), 315–368 (1990). CrossRefzbMATHGoogle Scholar
  9. 9.
    Lorenz, R., Mauser, S., Juhás, G.: How to synthesize nets from languages: a survey. In: WSC, pp. 637–647 (2007).
  10. 10.
    Schlachter, U.: Petri net synthesis for restricted classes of nets. In: Kordon, F., Moldt, D. (eds.) PETRI NETS 2016. LNCS, vol. 9698, pp. 79–97. Springer, Cham (2016). CrossRefGoogle Scholar
  11. 11.
    Schlachter, U., Wimmel, H.: k-bounded Petri net synthesis from MTS. In: Meyer, R., Nestmann, U. (eds.) CONCUR 2017. LIPIcs, vol. 85, pp. 6:1–6:15. Schloss Dagstuhl (2017).
  12. 12.
    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, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 368–387. Springer, Heidelberg (2008). CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computing ScienceUniversität OldenburgOldenburgGermany

Personalised recommendations