Saturation Enhanced with Conditional Locality: Application to Petri Nets

  • Vince MolnárEmail author
  • István Majzik
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11522)


The saturation algorithm for symbolic state space generation has proved to be an efficient way to tackle the state space explosion problem in the verification of concurrent, asynchronous systems. Since its original publication in 2001, several variants and extensions have been introduced. The reason for altering the algorithm in these variants is often specific to how it handles transitions. Saturation heavily relies on the notion of locality: transitions tend to affect only some of the state variables. The saturation effect, however, can be achieved and even enhanced with a weaker notion of locality, which we call conditional locality. In this paper, we define a generalized version of the saturation algorithm (GSA) for multi-valued decision diagrams that works with conditional locality and show that it enables the direct usage of transition relations that previously required a specialized algorithm such as variants of constrained saturation. Focusing on Petri nets, we also empirically demonstrate on models of the Model Checking Contest that the GSA often outperforms the original saturation algorithm whenever conditional locality can be exploited and has virtually no overhead for other models.


Generalized saturation Symbolic model checking Formal verification Conditional locality 



This work has been partially supported by Nemzeti Tehetség Program, Nemzet Fiatal Tehetségeiért Ösztöndíj 2018 (NTP-NFTÖ-18).


  1. 1.
    Amparore, E.G., Donatelli, S., Beccuti, M., Garbi, G., Miner, A.S.: Decision diagrams for Petri nets: a comparison of variable ordering algorithms. Trans. Petri Nets Other Models Concurr. 13, 73–92 (2018)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: \(10^{20}\) states and beyond. Inf. Comput. 98(2), 142–170 (1992)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ciardo, G., Lüttgen, G., Siminiceanu, R.: Saturation: an efficient iteration strategy for symbolic state-space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 328–342. Springer, Heidelberg (2001). Scholar
  4. 4.
    Ciardo, G., Marmorstein, R., Siminiceanu, R.: The saturation algorithm for symbolic state-space exploration. Int. J. Softw. Tools Technol. Transf. 8(1), 4–25 (2006)CrossRefGoogle Scholar
  5. 5.
    Ciardo, G., Yu, A.J.: Saturation-based symbolic reachability analysis using conjunctive and disjunctive partitioning. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 146–161. Springer, Heidelberg (2005). Scholar
  6. 6.
    Hamez, A., Thierry-Mieg, Y., Kordon, F.: Hierarchical set decision diagrams and automatic saturation. In: van Hee, K.M., Valk, R. (eds.) PETRI NETS 2008. LNCS, vol. 5062, pp. 211–230. Springer, Heidelberg (2008). Scholar
  7. 7.
    Kordon, F., et al.: Complete Results for the 2018 Edition of the Model Checking Contest, June 2018.
  8. 8.
    Marussy, K., Molnár, V., Vörös, A., Majzik, I.: Getting the priorities right: saturation for prioritised Petri nets. In: van der Aalst, W., Best, E. (eds.) PETRI NETS 2017. LNCS, vol. 10258, pp. 223–242. Springer, Cham (2017). Scholar
  9. 9.
    Meijer, J., Kant, G., Blom, S., van de Pol, J.: Read, write and copy dependencies for symbolic model checking. In: Yahav, E. (ed.) HVC 2014. LNCS, vol. 8855, pp. 204–219. Springer, Cham (2014). Scholar
  10. 10.
    Miner, A.S.: Implicit GSPN reachability set generation using decision diagrams. Perform. Eval. 56(1–4), 145–165 (2004)CrossRefGoogle Scholar
  11. 11.
    Molnár, V., Vörös, A., Darvas, D., Bartha, T., Majzik, I.: Component-wise incremental LTL model checking. Form. Asp. Comput. 28(3), 345–379 (2016)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Zhao, Y., Ciardo, G.: Symbolic CTL model checking of asynchronous systems using constrained saturation. In: Liu, Z., Ravn, A.P. (eds.) ATVA 2009. LNCS, vol. 5799, pp. 368–381. Springer, Heidelberg (2009). Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Fault Tolerant Systems Research Group, Department of Measurement and Information SystemsBudapest University of Technology and EconomicsBudapestHungary
  2. 2.MTA-BME Lendület Cyber-Physical Systems Research GroupBudapestHungary

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