Complexity in Simplicity: Flexible Agent-Based State Space Exploration

  • Jacob I. Rasmussen
  • Gerd Behrmann
  • Kim G. Larsen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4424)


In this paper, we describe a new flexible framework for state space exploration based on cooperating agents. The idea is to let various agents with different search patterns explore the state space individually and communicate information about fruitful subpaths of the search tree to each other. That way very complex global search behavior is achieved with very simple local behavior. As an example agent behavior, we propose a novel anytime randomized search strategy called frustration search. The effectiveness of the framework is illustrated in the setting of priced timed automata on a number of case studies.


State Space Model Check Symbolic State Hybrid Automaton Beam Search 


  1. 1.
    Abdeddaim, Y., Kerbaa, A., Maler, O.: Task graph scheduling using timed automata. In: Proc. of the International Parallel and Distributed Processing Symposium (IPDPS) (2003)Google Scholar
  2. 2.
    Alur, R., Dill, D.: Automata for modelling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  3. 3.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In Proc. of Hybrid Systems: Computation and Control. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Beasley, J.E., et al.: Scheduling aircraft landings - the static case. Transportation Science 34(2), 180–197 (2000)MATHCrossRefGoogle Scholar
  5. 5.
    Behrmann, G., et al.: Scheduling lacquer production by reachability analysis – a case study. In: Workshop on Parallel and Distributed Real-Time Systems 2005, p. 140. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  6. 6.
    Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Optimal scheduling using priced timed automata. SIGMETRICS Perform. Eval. Rev. 32(4), 34–40 (2005)CrossRefGoogle Scholar
  7. 7.
    Brihaye, T., Bruyère, V., Raskin, J.-F.: Model-checking weighted timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 277–292. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Fehnker, A.: Citius, Vilius, Melius - Guiding and Cost-Optimality in Model Checking of Timed and Hybrid Systems. IPA Dissertation Series, University of Nijmegen (2002)Google Scholar
  9. 9.
    Glover, F.: Tabu search-part I. ORSA Jour. on Computing 1(3), 190–206 (1989)MATHGoogle Scholar
  10. 10.
    Glover, F.: Tabu search-part II. ORSA Jour. on Computing 2(1), 4–32 (1990)MATHGoogle Scholar
  11. 11.
    Grosu, R., Smolka, S.A.: Monte carlo model checking. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 271–286. Springer, Heidelberg (2005)Google Scholar
  12. 12.
    Hart, P.E., Nilsson, N.J., Raphael, B.: A formal basis for the heuristic determination of minimum cost paths. IEEE Transactions on Systems Science and Cybernetics 4(2), 100–107 (1968)CrossRefGoogle Scholar
  13. 13.
    Hendriks, M.: Model Checking Timed Automata - Techniques and Applications. IPA Dissertation Series, University of Nijmegen (2006)Google Scholar
  14. 14.
    Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)Google Scholar
  15. 15.
    Hromkovic, J., Oliva, W.M.: Algorithmics for Hard Problems. Springer, New York (2002)Google Scholar
  16. 16.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Larsen, K., et al.: As cheap as possible: Efficient cost-optimal reachability for priced timed automata. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, p. 493. Springer, Heidelberg (2001)Google Scholar
  18. 18.
    Rasmussen, J., Larsen, K., Subramani, K.: Resource-optimal scheduling using priced timed automata. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 220–235. Springer, Heidelberg (2004)Google Scholar
  19. 19.
    Wolpert, D.H., Macready, W.G.: No free lunch theorems for search. Technical Report SFI-TR-95-02-010, Santa Fe Institute, Santa Fe, NM (1995)Google Scholar
  20. 20.
    Zhou, R., Hansen, E.A.: Beam-stack search: Integrating backtracking with beam search. In: Proc. of International Conference on Automated Planning and Scheduling, pp. 90–98. AAAI Press, Menlo Park (2005)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Jacob I. Rasmussen
    • 1
  • Gerd Behrmann
    • 1
  • Kim G. Larsen
    • 1
  1. 1.Department of Computer Science, Aalborg UniversityDenmark

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