On Liveness and Deadlockability in Subclasses of Weighted Petri Nets

  • Thomas HujsaEmail author
  • Raymond Devillers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10258)


Structural approaches have greatly simplified the analysis of intractable properties in Petri nets, notably liveness. In this paper, we further develop these structural methods in particular weighted subclasses of Petri nets to analyze liveness and deadlockability, the latter property being a strong form of non-liveness.

For homogeneous join-free nets, from the analysis of specific substructures, we provide the first polynomial-time characterizations of structural liveness and structural deadlockability, expressing respectively the existence of a live marking and the deadlockability of every marking.

For the join-free class, assuming structural boundedness and leaving out the homogeneity constraint, we show that liveness is not monotonic, meaning not always preserved upon any increase of a live marking.

Finally, we use this new material to correct a flaw in the proof of a previous characterization of monotonic liveness and boundedness for homogeneous asymmetric-choice nets, published in 2004 and left unnoticed.


Structural analysis Weighted Petri net Deadlockability Liveness Boundedness Monotonicity Fork-attribution Join-free Communication-free Synchronization-free Asymmetric-choice 


  1. 1.
    Barkaoui, K., Couvreur, J.-M., Klai, K.: On the equivalence between liveness and deadlock-freeness in Petri nets. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 90–107. Springer, Heidelberg (2005). doi: 10.1007/11494744_7 CrossRefGoogle Scholar
  2. 2.
    Barkaoui, K., Minoux, M.: A polynomial-time graph algorithm to decide liveness of some basic classes of bounded Petri nets. In: Jensen, K. (ed.) ICATPN 1992. LNCS, vol. 616, pp. 62–75. Springer, Heidelberg (1992). doi: 10.1007/3-540-55676-1_4 CrossRefGoogle Scholar
  3. 3.
    Barkaoui, K., Pradat-Peyre, J.-F.: On liveness and controlled siphons in Petri nets. In: Billington, J., Reisig, W. (eds.) ICATPN 1996. LNCS, vol. 1091, pp. 57–72. Springer, Heidelberg (1996). doi: 10.1007/3-540-61363-3_4 CrossRefGoogle Scholar
  4. 4.
    Cheng, A., Esparza, J., Palsberg, J.: Complexity results for 1-safe nets. In: Shyamasundar, R.K. (ed.) FSTTCS 1993. LNCS, vol. 761, pp. 326–337. Springer, Heidelberg (1993). doi: 10.1007/3-540-57529-4_66 CrossRefGoogle Scholar
  5. 5.
    Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge Tracts in Theoretical Computer Science, vol. 40. Cambridge University Press, New York (1995)CrossRefzbMATHGoogle Scholar
  6. 6.
    Esparza, J.: Decidability and complexity of Petri net problems – an introduction. In: Reisig, W., Rozenberg, G. (eds.) ACPN 1996. LNCS, vol. 1491, pp. 374–428. Springer, Heidelberg (1998). doi: 10.1007/3-540-65306-6_20 CrossRefGoogle Scholar
  7. 7.
    Esparza, J., Nielsen, M.: Decidability issues for Petri nets–a survey. BRICS Rep. Ser. (8) (1994)Google Scholar
  8. 8.
    Heiner, M., Mahulea, C., Silva, M.: On the importance of the deadlock trap property for monotonic liveness. In: International Workshop on Biological Processes and Petri nets (BioPPN), A satellite event of Petri Nets 2010 (2010)Google Scholar
  9. 9.
    Hujsa, T., Delosme, J.M., Munier-Kordon, A.: Polynomial sufficient conditions of well-behavedness and home markings in subclasses of weighted Petri nets. Trans. Embed. Comput. Syst. 13, 1–25 (2014)CrossRefGoogle Scholar
  10. 10.
    Hujsa, T., Delosme, J.M., Munier-Kordon, A.: On liveness and reversibility of equal-conflict Petri nets. Fundam. Inf. 146(1), 83–119 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Jiao, L., Cheung, T.Y., Lu, W.: On liveness and boundedness of asymmetric choice nets. Theor. Comput. Sci. 311(1–3), 165–197 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lee, E.A., Messerschmitt, D.G.: Synchronous data flow. Proc. IEEE 75(9), 1235–1245 (1987)CrossRefGoogle Scholar
  13. 13.
    Lipton, R.: The reachability problem requires exponential space. Technical report 62, Department of Computer Science, Yale University (1976)Google Scholar
  14. 14.
    Mayr, E.W., Weihmann, J.: Results on equivalence, boundedness, liveness, and covering problems of BPP-Petri nets. In: Colom, J.-M., Desel, J. (eds.) PETRI NETS 2013. LNCS, vol. 7927, pp. 70–89. Springer, Heidelberg (2013). doi: 10.1007/978-3-642-38697-8_5 CrossRefGoogle Scholar
  15. 15.
    Mayr, E.W., Weihmann, J.: Complexity results for problems of communication-free Petri nets and related formalisms. Fundam. Inf. 137(1), 61–86 (2015)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Recalde, L., Teruel, E., Silva, M.: Modeling and analysis of sequential processes that cooperate through buffers. IEEE Trans. Robot. Autom. 14(2), 267–277 (1998)CrossRefGoogle Scholar
  17. 17.
    Sifakis, J.: Structural properties of Petri nets. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 474–483. Springer, Heidelberg (1978). doi: 10.1007/3-540-08921-7_95 CrossRefGoogle Scholar
  18. 18.
    Silva, M., Teruel, 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). doi: 10.1007/3-540-65306-6_19 CrossRefGoogle Scholar
  19. 19.
    Teruel, E.: Structure Theory of Weighted Place/Transition Net Systems: The Equal Conflict Hiatus. Ph.D. thesis, DIEI. University of Zaragoza, Spain (1994)Google Scholar
  20. 20.
    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)CrossRefGoogle Scholar
  21. 21.
    Teruel, E., Silva, M.: Liveness and home states in equal conflict systems. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, pp. 415–432. Springer, Heidelberg (1993). doi: 10.1007/3-540-56863-8_59 CrossRefGoogle Scholar
  22. 22.
    Teruel, E., Silva, M.: Structure theory of equal conflict systems. Theor. Comput. Sci. 153(1&2), 271–300 (1996)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computing ScienceCarl von Ossietzky Universität OldenburgOldenburgGermany
  2. 2.Département d’InformatiqueUniversité Libre de BruxellesBrusselsBelgium

Personalised recommendations