Model Checking Concurrency and Causality

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10258)


We consider a spectrum of properties proposed in [14], that is related to causality and concurrency between a pair of given transitions in a place/transition net. For each of these properties, we ask whether it can be verified using an ordinary, interleaving based, model checker. With a systematic approach based on two constructions, we reduce 75% of the properties in the spectrum to a reachability problem. We have to leave the remaining 25% as open problems.




  1. 1.
    Best, E., Devillers, R.: Sequential and concurrent behaviour in Petri net theory. Theoret. Comput. Sci. 55(1), 87–136 (1987)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Best, E., Fernandez, C.: Nonsequential Processes: A Petri Net View. EATCS Monographs on Theoretical Computer Science. Springer, Heidelberg (1988)CrossRefGoogle Scholar
  3. 3.
    Brauer, W., Reisig, W.: Carl adam Petri and “Petri nets”. Fundam. Concepts Comput. Sci. 3, 129–139 (2009)CrossRefGoogle Scholar
  4. 4.
    Esparza, J., Heljanko, K.: Unfoldings - A Partial-Order Approach to Model Checking. EATCS Monographs in Theoretical Computer Science. Springer, Heidelberg (2008)MATHGoogle Scholar
  5. 5.
    Goltz, U., Reisig, W.: The non-sequential behaviour of Petri nets. Inf. Control 57(2/3), 125–147 (1983)CrossRefMATHGoogle Scholar
  6. 6.
    Grahlmann, B.: The PEP tool. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 440–443. Springer, Heidelberg (1997). doi: 10.1007/3-540-63166-6_43 CrossRefGoogle Scholar
  7. 7.
    Heiner, M., Rohr, C., Schwarick, M., Tovchigrechko, A.A.: MARCIE’s secrets of efficient model checking. In: Koutny, M., Desel, J., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency XI. LNCS, vol. 9930, pp. 286–296. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53401-4_14 CrossRefGoogle Scholar
  8. 8.
    Jensen, J.F., Nielsen, T., Oestergaard, L.K., Srba, J.: TAPAAL and reachability analysis of P/T nets. In: Koutny, M., Desel, J., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency XI. LNCS, vol. 9930, pp. 307–318. Springer, Heidelberg (2016). doi: 10.1007/978-3-662-53401-4_16 CrossRefGoogle Scholar
  9. 9.
    Jensen, K.: Coloured Petri Nets - Basic Concepts, Analysis Methods and Practical Use - EATCS Monographs in Theoretical Computer Science, vol. 1, 2nd edn. Springer, Heidelberg (1996)Google Scholar
  10. 10.
    Khomenko, V.: PUNF–Petri net unfolder.
  11. 11.
    McMillan, K.L.: A technique of state space search based on unfolding. Formal Methods Syst. Des. 6(1), 45–65 (1995)CrossRefMATHGoogle Scholar
  12. 12.
    Nielsens, M., Plotkin, G.D., Winskel, G.: Petri nets, event structures and domains. Theoret. Comput. Sci. 13(1), 85–108 (1981)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Petri, C.A.: Kommunikation mit Automaten. Dissertation, Schriften des IIM 2, Rheinisch-Westfälisches Institut für Instrumentelle Mathematik an der Universität Bonn, Bonn (1962)Google Scholar
  14. 14.
    Polyvyanyy, A., Weidlich, M., Conforti, R., Rosa, M., Hofstede, A.H.M.: The 4C spectrum of fundamental behavioral relations for concurrent systems. In: Ciardo, G., Kindler, E. (eds.) PETRI NETS 2014. LNCS, vol. 8489, pp. 210–232. Springer, Cham (2014). doi: 10.1007/978-3-319-07734-5_12 CrossRefGoogle Scholar
  15. 15.
    Schwoon, S.: Mole–a Petri net unfolder.
  16. 16.
    Hofstede, A.H.M., Ouyang, C., Rosa, M., Song, L., Wang, J., Polyvyanyy, A.: APQL: a process-model query language. In: Song, M., Wynn, M.T., Liu, J. (eds.) AP-BPM 2013. LNBIP, vol. 159, pp. 23–38. Springer, Cham (2013). doi: 10.1007/978-3-319-02922-1_2 CrossRefGoogle Scholar
  17. 17.
    Thierry-Mieg, Y.: Symbolic model-checking using ITS-tools. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 231–237. Springer, Heidelberg (2015). doi: 10.1007/978-3-662-46681-0_20 Google Scholar
  18. 18.
    M. Weidlich. Behavioural profiles: a relational approach to behaviour consistency. Ph.D. thesis, University of Potsdam (2011)Google Scholar
  19. 19.
    Wimmel, H., Wolf, K.: Applying CEGAR to the Petri net state equation. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 224–238. Springer, Heidelberg (2011). doi: 10.1007/978-3-642-19835-9_19 CrossRefGoogle Scholar
  20. 20.
    Wolf, K.: Generating Petri net state spaces. In: Kleijn, J., Yakovlev, A. (eds.) ICATPN 2007. LNCS, vol. 4546, pp. 29–42. Springer, Heidelberg (2007). doi: 10.1007/978-3-540-73094-1_5 CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Institut Für InformatikUniversität RostockRostockGermany

Personalised recommendations