Selective Approaches for Solving Weak Games

  • Malte Helmert
  • Robert Mattmüller
  • Sven Schewe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4218)


Model-checking alternating-time properties has recently attracted much interest in the verification of distributed protocols. While checking the validity of a specification in alternating-time temporal logic (ATL) against an explicit model is cheap (linear in the size of the formula and the model), the problem becomes EXPTIME-hard when symbolic models are considered. Practical ATL model-checking therefore often consumes too much computation time to be tractable.

In this paper, we describe a novel approach for ATL model-checking, which constructs an explicit weak model-checking game on-the-fly. This game is then evaluated using heuristic techniques inspired by efficient evaluation algorithms for and/or-trees.

To show the feasibility of our approach, we compare its performance to the ATL model-checking system MOCHA on some practical examples. Using very limited heuristic guidance, we achieve a significant speedup on these benchmarks.


Model Check Reachable State Initial Vertex Selective Approach Computation Tree Logic 
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.
    Allis, L.V., van der Meulen, M., van der Herik, H.J.: Proof-number search. Artificial Intelligence 66(1), 91–124 (1994)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Alur, R., Henzinger, T.A., Mang, F.Y.C., Qadeer, S., Rajamani, S.K., Tasiran, S.: Mocha: Modularity in model checking. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 521–525. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  4. 4.
    Andersen, H.R.: Model checking and boolean graphs. Theor. Comput. Sci. 126(1), 3–30 (1994)MATHCrossRefGoogle Scholar
  5. 5.
    Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 1020 states and beyond. Information and Computation 98(2), 142–170 (1992)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chadha, R., Kremer, S., Scedrov, A.: Analysis of multi-party contract signing. Technical Report 516, Université Libre de Bruxelles (2004)Google Scholar
  7. 7.
    Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Proc. IBM Workshop on Logics of Programs, pp. 52–71 (1981)Google Scholar
  8. 8.
    Cleaveland, R., Steffen, B.: A linear-time model-checking algorithm for the alternation-free modal μ-calculus. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 48–58. Springer, Heidelberg (1992)Google Scholar
  9. 9.
    Emerson, E.A., Jutla, C.S.: Tree automata, μ-calculus and determinacy. In: Proc. FOCS, pp. 368–377 (1991)Google Scholar
  10. 10.
    Garay, J.A., MacKenzie, P.D.: Abuse-free multi-party contract signing. In International Symposium on Distributed Computing. In: Jayanti, P. (ed.) DISC 1999. LNCS, vol. 1693, pp. 151–165. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  11. 11.
    Hoffmann, J., Nebel, B.: The FF planning system: Fast plan generation through heuristic search. Journal of Artificial Intelligence Research 14, 253–302 (2001)MATHGoogle Scholar
  12. 12.
    Holzmann, G.J.: The model checker SPIN. Software Engineering 23(5), 279–295 (1997)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Knuth, D.E., Moore, R.W.: An analysis of alpha-beta pruning. Artificial Intelligence 6(4), 293–326 (1975)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Kremer, S.: Formal Analysis of Optimistic Fair Exchange Protocols. PhD thesis, Université Libre de Bruxelles, Brussels, Belgium (December 2003)Google Scholar
  15. 15.
    Kremer, S., Raskin, J.-F.: A game-based verification of non-repudiation and fair exchange protocols. Journal of Computer Security 11(3), 399–430 (2003)Google Scholar
  16. 16.
    Mahimkar, A., Shmatikov, V.: Game-based analysis of denial-of-service prevention protocols. In: IEEE Computer Security Foundations Workshop, pp. 287–301 (2005)Google Scholar
  17. 17.
    Ryan, M., Schobbens, P.-Y.: Agents and roles: Refinement in alternating-time temporal logic. In: Meyer, J.-J.C., Tambe, M. (eds.) ATAL 2001. LNCS (LNAI), vol. 2333, pp. 100–114. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    van der Hoek, W., Lomuscio, A., Wooldridge, M.: On the complexity of practical ATL model checking. In: Proc. AAMAS (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Malte Helmert
    • 1
  • Robert Mattmüller
    • 1
  • Sven Schewe
    • 2
  1. 1.Albert-Ludwigs-Universität FreiburgFreiburgGermany
  2. 2.Universität des SaarlandesSaarbrückenGermany

Personalised recommendations