Model-Based Variable and Transition Orderings for Efficient Symbolic Model Checking

  • Wendy Johnston
  • Kirsten Winter
  • Lionel van den Berg
  • Paul Strooper
  • Peter Robinson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4085)


The symbolic model checker NuSMV has been used to check safety properties for railway interlockings. When the size of the models increased, the model checking efficiency decreased dramatically to a point at which the verification failed due to lack of memory. At that point the models we could check were still small in the real world of railway interlockings. Various standard options to the NuSMV model checker were tried, mostly without significant improvement. However, the analysis of our model provided information on how to optimise the variable orderings and also the ordering and clustering of the partitioned transition relation. The NuSMV code was adapted to enable user control for ordering and clustering of transitions. This replacement of the tool’s generic algorithm improved efficiency enormously, enabling the checking of safety properties for very large models. This paper discusses how the characteristics of our model are used to find the optimised parameters.


Symbolic model checking Binary Decision Diagrams image computation partitioned transition relations clustering railway interlockings 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Robinson, N., Barney, D., Kearney, P., Nikandros, G., Tombs, D.: Automatic generation and verification of design specification. In: Proc. of Int. Symp. of the International Council On Systems Engineering (INCOSE) (2001)Google Scholar
  2. 2.
    Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV 2: an OpenSource tool for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 359–364. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Winter, K., Robinson, N.J.: Modelling large interlocking systems and model checking small ones. In: Oudshoorn, M. (ed.) Proc. of Australasian Computer Science Conference (ACSC 2003). Australian Computer Science Communications, vol. 16 (2003)Google Scholar
  4. 4.
    McMillan, K.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)zbMATHGoogle Scholar
  5. 5.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
  6. 6.
    Burch, J.R., Clarke, E.M., Long, D.E.: Symbolic model checking with partitioned transition relations. In: Halaas, A., Denyer, P.B. (eds.) Proc. of Int. Conference on Very Large Scale Integration, pp. 49–58. North-Holland, Amsterdam (1991)Google Scholar
  7. 7.
    Geist, D., Beer, I.: Efficient model checking by automated ordering of transition relation. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 299–310. Springer, Heidelberg (1994)Google Scholar
  8. 8.
    Ranjan, R., Aziz, A., Brayton, R., Plessier, B., Pixley, C.: Efficient BDD algorithms for FSM synthesis and verification. In: Proc. of IEEE/ACM Int. Workshop on Logic Synthesis (1995)Google Scholar
  9. 9.
    Moon, I., Hachtel, G.D., Somenzi, F.: Border-block triangular form and conjunction schedule in image computation. In: Johnson, S.D., Hunt Jr., W.A. (eds.) FMCAD 2000. LNCS, vol. 1954, pp. 73–90. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  10. 10.
    Somenzi, F.: CUDD: CU Decision Diagram package — release 2.3.0. In: Department of Electrical and Computer Engineering — University of Colorado at Boulder (September 1998)Google Scholar
  11. 11.
    Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Transactions On Computers C-35(8) (1986)Google Scholar
  12. 12.
    Lewis, G., Comella-Dorda, S., Gluch, D., Hudak, J., Weinstock, C.: Model-based verification: Analysis guidelines. Technical Report CMU/SEI-2001-TN-028, Carnegie Mellon Software Engineering Institute (2001)Google Scholar
  13. 13.
    Chan, W., Anderson, R.J., Beame, P., Burns, S., Modugno, F., Notkin, D., Reese, J.D.: Model checking large software specifications. IEEE Transactions on Software Engineering 24(7), 498–520 (1998)CrossRefGoogle Scholar
  14. 14.
    Kamhi, G., Fix, L.: Adaptive variable reordering for symbolic model checking. In: Proc. of IEEE/ACM Int. Conference on Computer-aided design (ICCAD 1998), pp. 359–365. ACM Press, New York (1998)CrossRefGoogle Scholar
  15. 15.
    Lu, Y., Jain, J., Clarke, E., Fujita, M.: Efficient variable ordering using a BDD based sampling. In: Proc. of Int. Conference on Design automation (DAC 2000), pp. 687–692. ACM Press, New York (2000)CrossRefGoogle Scholar
  16. 16.
    Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Proc. of IEEE/ACM Int. Conference on Computer-aided design (ICCAD 1993), pp. 42–47. IEEE Computer Society Press, Los Alamitos (1993)CrossRefGoogle Scholar
  17. 17.
    Winter, K., Johnston, W., Robinson, P., Strooper, P., van den Berg, L.: Tool support for checking railway interlocking designs. In: Cant, T. (ed.) 10th Australian Workshop on Safety Related Programmable Systems (SCS 2005), vol. 55, Australian Computer Society, Inc. (to appear, 2005)Google Scholar
  18. 18.
    Cavda, R., Cimatti, A., Olivetti, E., Pistore, M., Roveri, M.: NuSMV 2.0 User Manual (2001),
  19. 19.
    Eisner, C.: Using symbolic model checking to verify the railway stations of hoorn-kersenboogerd and heerhugowaard. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 97–109. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  20. 20.
    Huber, M., King, S.: Towards an integrated model checker for railway signalling data. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME 2002. LNCS, vol. 2391, pp. 204–223. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  21. 21.
    Wang, C., Hachtel, G.D., Somenzi, F.: The compositional far side of image computation. In: Proc. of IEEE/ACM Int. Conference on Computer-Aided Design (ICCAD 2003), pp. 334–340. IEEE Computer Society, Los Alamitos (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Wendy Johnston
    • 1
  • Kirsten Winter
    • 1
  • Lionel van den Berg
    • 1
  • Paul Strooper
    • 1
  • Peter Robinson
    • 1
  1. 1.School of ITEEUniversity of QueenslandBrisbane (St.Lucia)Australia

Personalised recommendations