Infinite Runs in Weighted Timed Automata with Energy Constraints

  • Patricia Bouyer
  • Uli Fahrenberg
  • Kim G. Larsen
  • Nicolas Markey
  • Jiří Srba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5215)


We study the problems of existence and construction of infinite schedules for finite weighted automata and one-clock weighted timed automata, subject to boundary constraints on the accumulated weight. More specifically, we consider automata equipped with positive and negative weights on transitions and locations, corresponding to the production and consumption of some resource (e.g. energy). We ask the question whether there exists an infinite path for which the accumulated weight for any finite prefix satisfies certain constraints (e.g. remains between 0 and some given upper-bound). We also consider a game version of the above, where certain transitions may be uncontrollable.


Polynomial Time Winning Strategy Negative Weight Energy Constraint Existential Problem 
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., Bernadsky, M., Madhusudan, P.: Optimal reachability in weighted timed games. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 122–133. Springer, Heidelberg (2004)Google Scholar
  2. 2.
    Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.: Minimum-cost reachability for priced timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  4. 4.
    Bouyer, P., Brihaye, Th., Bruyère, V., Raskin, J.-F.: On the optimal reachability problem. Formal Methods in System Design 31(2), 135–175 (2007)zbMATHCrossRefGoogle Scholar
  5. 5.
    Bouyer, P., Brihaye, Th., Markey, N.: Improved undecidability results on weighted timed automata. Inf. Proc. Letters 98(5), 188–194 (2006)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Bouyer, P., Brinksma, E., Larsen, K.G.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G.: Optimal strategies in priced timed game automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 148–160. Springer, Heidelberg (2004)Google Scholar
  8. 8.
    Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. Research Report LSV-08-23, Laboratoire Spécification et Vérification, ENS Cachan, France (2008),
  9. 9.
    Bouyer, P., Larsen, K.G., Markey, N.: Model-checking one-clock priced timed automata. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 108–122. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  10. 10.
    Bouyer, P., Larsen, K.G., Markey, N., Rasmussen, J.I.: Almost optimal strategies in one-clock priced timed automata. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 345–356. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  11. 11.
    Bouyer, P., Markey, N.: Costs are expensive! In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 53–68. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  12. 12.
    Brihaye, Th., Bruyère, V., Raskin, J.-F.: Model-checking for 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
  13. 13.
    Brihaye, Th., Bruyère, V., Raskin, J.-F.: On optimal timed strategies. In: Ramanujam, R., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 49–64. Springer, Heidelberg (2005)Google Scholar
  14. 14.
    Chandra, A.K., Kozen, D.C., Stockmeyer, L.J.: Alternation. J. ACM 28(1), 114–133 (1981)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ehrenfeucht, A., Mycielski, J.: Positional strategies for mean payoff games. Int. J. Game Theory 8(2), 109–113 (1979)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Fahrenberg, U., Larsen, K.G.: Discount-optimal infinite runs in priced timed automata (submitted, 2008)Google Scholar
  17. 17.
    Jurdziński, M.: Deciding the winner in parity games is in UP∩co-UP. Inf. Proc. Letters 68(3), 119–124 (1998)CrossRefGoogle Scholar
  18. 18.
    Jurdziński, M., Laroussinie, F., Sproston, J.: Model checking probabilistic timed automata with one or two clocks. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 170–184. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Laroussinie, F., Markey, N., Schnoebelen, Ph.: Model checking timed automata with one or two clocks. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 387–401. Springer, Heidelberg (2004)Google Scholar
  20. 20.
    Larsen, K.G., Rasmussen, J.I.: Optimal conditional scheduling for multi-priced timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 234–249. Springer, Heidelberg (2005)Google Scholar
  21. 21.
    Martin, D.: Borel determinacy. Annals Math. 102(2), 363–371 (1975)CrossRefGoogle Scholar
  22. 22.
    Papadimitriou, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Patricia Bouyer
    • 1
  • Uli Fahrenberg
    • 2
  • Kim G. Larsen
    • 2
  • Nicolas Markey
    • 1
  • Jiří Srba
    • 2
  1. 1.Lab. Spécification et VérificationCNRS & ENS CachanFrance
  2. 2.Dept. of Computer ScienceAalborg UniversityDenmark

Personalised recommendations