Abstract
We study techniques to overcome the state space explosion problem in CTL model checking of Petri nets. Classical state space pruning approaches like partial order reductions and structural reductions become less efficient with the growing size of the CTL formula. The reason is that the more places and transitions are used as atomic propositions in a given formula, the more of the behaviour (interleaving) becomes relevant for the validity of the formula. We suggest several methods to reduce the size of CTL formulae, while preserving their validity. By these methods, we significantly increase the benefits of structural and partial order reductions, as the combination of our techniques can achive up to 60% average reduction in formulae sizes. The algorithms are implemented in the open-source verification tool TAPAAL and we document the efficiency of our approach on a large benchmark of Petri net models and queries from the Model Checking Contest 2017.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
We use the current development snapshots of LoLA (based on version 2.0) and Sara (based on version 1.14), kindly provided by the LoLA and Sara development team.
References
Avrunin, G.S., Buy, U.A., Corbett, J.C.: Integer programming in the analysis of concurrent systems. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 92–102. Springer, Heidelberg (1992). https://doi.org/10.1007/3-540-55179-4_10
Avrunin, G.S., Buy, U.A., Corbett, J.C., Dillon, L.K., Wileden, J.C.: Automated analysis of concurrent systems with the constrained expression toolset. IEEE Trans. Softw. Eng. 17(11), 1204–1222 (1991)
Berkelaar, M., Eikland, K., Notebaert, P., et al.: lpsolve: open source (mixed-integer) linear programming system. Eindhoven University of Technology (2004)
Blondin, M., Finkel, A., Haase, C., Haddad, S.: Approaching the coverability problem continuously. In: Chechik, M., Raskin, J.-F. (eds.) TACAS 2016. LNCS, vol. 9636, pp. 480–496. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-49674-9_28
Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0025774
Clarke, E.M., Emerson, E.A., Sifakis, J.: Model checking: algorithmic verification and debugging. Commun. ACM 52(11), 74–84 (2009)
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. (TOPLAS) 8(2), 244–263 (1986)
Corbett, J.C., Avrunin, G.S.: Using integer programming to verify general safety and liveness properties. Formal Methods Syst. Des. 6(1), 97–123 (1995)
Dalsgaard, A.E., Enevoldsen, S., Fogh, P., Jensen, L.S., Jepsen, T.S., Kaufmann, I., Larsen, K.G., Nielsen, S.M., Olesen, M.C., Pastva, S., Srba, J.: Extended dependency graphs and efficient distributed fixed-point computation. In: van der Aalst, W., Best, E. (eds.) PETRI NETS 2017. LNCS, vol. 10258, pp. 139–158. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-57861-3_10
David, A., Jacobsen, L., Jacobsen, M., Jørgensen, K.Y., Møller, M.H., Srba, J.: TAPAAL 2.0: Integrated development environment for timed-arc Petri nets. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 492–497. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28756-5_36
Esparza, J., Melzer, S.: Verification of safety properties using integer programming: beyond the state equation. Formal Methods Syst. Des. 16(2), 159–189 (2000)
Geffroy, T., Leroux, J., Sutre, G.: Occam’s Razor applied to the Petri net coverability problem. In: Larsen, K.G., Potapov, I., Srba, J. (eds.) RP 2016. LNCS, vol. 9899, pp. 77–89. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45994-3_6
Hack, M.H.T.: Analysis of production schemata by Petri nets. Technical report, DTIC Document (1972)
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). https://doi.org/10.1007/978-3-662-53401-4_16
Kordon, F., Garavel, H., Hillah, L.M., Hulin-Hubard, F., Berthomieu, B., Ciardo, G., Colange, M., Dal Zilio, S., Amparore, E., Beccuti, M., Liebke, T., Meijer, J., Miner, A., Rohr, C., Srba, J., Thierry-Mieg, Y., van de Pol, J., Wolf, K.: Complete Results for the 2017 Edition of the Model Checking Contest, June 2017. http://mcc.lip6.fr/2017/results.php
Kristensen, L.M., Schmidt, K., Valmari, A.: Question-guided stubborn set methods for state properties. Formal Methods Syst. Des. 29(3), 215–251 (2006)
Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)
Murata, T., Koh, J.Y.: Reduction and expansion of live and safe marked graphs. IEEE Trans. Circ. Syst. 27(1), 68–70 (1980)
Nemhauser, G.L., Wolsey, L.A.: Integer Programming and Combinatorial Optimization. Wiley, Chichester (1992). Nemhauser, G.L., Savelsbergh, M.W.P., Sigismondi, G.S.: Constraint classification for mixed integer programming formulations. COAL Bull. 20, 8–12 (1988)
Schmidt, K.: Stubborn sets for standard properties. In: Donatelli, S., Kleijn, J. (eds.) ICATPN 1999. LNCS, vol. 1639, pp. 46–65. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48745-X_4
Schmidt, K.: Integrating low level symmetries into reachability analysis. In: Graf, S., Schwartzbach, M. (eds.) TACAS 2000. LNCS, vol. 1785, pp. 315–330. Springer, Heidelberg (2000). https://doi.org/10.1007/3-540-46419-0_22
Schmidt, K.: Narrowing Petri net state spaces using the state equation. Fundamenta Informaticae 47(3–4), 325–335 (2001)
Valmari, A.: Stubborn sets for reduced state space generation. In: Rozenberg, G. (ed.) ICATPN 1989. LNCS, vol. 483, pp. 491–515. Springer, Heidelberg (1991). https://doi.org/10.1007/3-540-53863-1_36
Valmari, A., Hansen, H.: Stubborn set intuition explained. In: Koutny, M., Kleijn, J., Penczek, W. (eds.) Transactions on Petri Nets and Other Models of Concurrency XII. LNCS, vol. 10470, pp. 140–165. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55862-1_7
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). https://doi.org/10.1007/978-3-642-19835-9_19
Wolf, K.: Running LoLA 2.0 in a model checking competition. In: Koutny, M., Desel, J., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency XI. LNCS, vol. 9930, pp. 274–285. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53401-4_13
Acknowledgements
We would like to thank Karsten Wolf and Torsten Liebke from Rostock University for providing us with the development snapshot of the latest version of LoLA and for their help with setting up the tool and answering our questions. The last author is partially affiliated with FI MU, Brno.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Bønneland, F., Dyhr, J., Jensen, P.G., Johannsen, M., Srba, J. (2018). Simplification of CTL Formulae for Efficient Model Checking of Petri Nets. In: Khomenko, V., Roux, O. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2018. Lecture Notes in Computer Science(), vol 10877. Springer, Cham. https://doi.org/10.1007/978-3-319-91268-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-91268-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-91267-7
Online ISBN: 978-3-319-91268-4
eBook Packages: Computer ScienceComputer Science (R0)