Local Model Checking of Weighted CTL with Upper-Bound Constraints

  • Jonas Finnemann Jensen
  • Kim Guldstrand Larsen
  • Jiří Srba
  • Lars Kaerlund Oestergaard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7976)


We present a symbolic extension of dependency graphs by Liu and Smolka in order to model-check weighted Kripke structures against the logic CTL with upper-bound weight constraints. Our extension introduces a new type of edges into dependency graphs and lifts the computation of fixed-points from boolean domain to nonnegative integers in order to cope with the weights. We present both global and local algorithms for the fixed-point computation on symbolic dependency graphs and argue for the advantages of our approach compared to the direct encoding of the model checking problem into dependency graphs. We implement all algorithms in a publicly available tool prototype and evaluate them on several experiments. The principal conclusion is that our local algorithm is the most efficient one with an order of magnitude improvement for model checking problems with a high number of “witnesses”.


Model Check Dependency Graph Local Algorithm Task Graph Atomic Proposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Dill, D.: Automata for modeling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  2. 2.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [7], pp. 49–62Google Scholar
  3. 3.
    Andersen, H.R.: Model checking and boolean graphs. Theoretical Computer Science 126(1), 3–30 (1994)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Kasahara Laboratory at Waseda University. Standard task graph set,
  5. 5.
    Bartlett, K.A., Scantlebury, R.A., Wilkinson, P.T.: A note on reliable full-duplex transmission over half-duplex links. Communications of the ACM 12(5), 260–261 (1969)CrossRefGoogle Scholar
  6. 6.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [7], pp. 147–161Google Scholar
  7. 7.
    Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.): HSCC 2001. LNCS, vol. 2034. Springer, Heidelberg (2001)Google Scholar
  8. 8.
    Bouyer, P., Larsen, K.G., Markey, N.: Model checking one-clock priced timed automata. Logical Methods in Computer Science 4(2) (2008)Google Scholar
  9. 9.
    Brihaye, T., Bruyère, V., Raskin, J.-F.: Model-checking for weighted timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT 2004. LNCS, vol. 3253, pp. 277–292. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Buchholz, P., Kemper, P.: Model checking for a class of weighted automata. Discrete Event Dynamic Systems 20, 103–137 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Chang, E., Roberts, R.: An improved algorithm for decentralized extrema-finding in circular configurations of processes. Commun. of ACM 22(5), 281–283 (1979)zbMATHCrossRefGoogle Scholar
  13. 13.
    Kwok, Y.-K., Ahmad, I.: Benchmarking and comparison of the task graph scheduling algorithms. Journal of Parallel and Distributed Computing 59(3), 381–422 (1999)zbMATHCrossRefGoogle Scholar
  14. 14.
    Laroussinie, F., Markey, N., Oreiby, G.: Model-checking timed ATL for durational concurrent game structures. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 245–259. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  15. 15.
    Liu, X., Ramakrishnan, C.R., Smolka, S.A.: Fully local and efficient evaluation of alternating fixed points (Extended abstract). In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 5–19. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  16. 16.
    Liu, X., Smolka, S.A.: Simple linear-time algorithms for minimal fixed points (extended abstract). In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 53–66. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  17. 17.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jonas Finnemann Jensen
    • 1
  • Kim Guldstrand Larsen
    • 1
  • Jiří Srba
    • 1
  • Lars Kaerlund Oestergaard
    • 1
  1. 1.Department of Computer ScienceAalborg UniversityAalborgDenmark

Personalised recommendations