Abstract
Priced timed (game) automata extend timed (game) automata with costs on both locations and transitions. In this paper we focus on reachability priced timed game automata and prove that the optimal cost for winning such a game is computable under conditions concerning the non-zenoness of cost. Under stronger conditions (strictness of constraints) we prove that in case an optimal strategy exists, we can compute a state-based winning optimal strategy.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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)
Alur, R., Courcoubetis, C., Henzinger, T.: Computing accumulated delays in real-time systems. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 181–193. Springer, Heidelberg (1993)
Alur, R., La Torre, S., Pappas, G.: 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)
Asarin, E., Maler, O.: As soon as possible: Time optimal control for timed automata. In: Vaandrager, F.W., van Schuppen, J.H. (eds.) HSCC 1999. LNCS, vol. 1569, pp. 19–30. Springer, Heidelberg (1999)
Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: Proc. IFAC Symp. System Structure and Control, pp. 469–474. Elsevier Science, Amsterdam (1998)
Behrmann, G., Fehnker, A., Hune, T., Larsen, K., 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)
Bouyer, P., Cassez, F., Fleury, E., Larsen, K.: Optimal Strategies on Priced Timed Game Automata. BRICS Report Series (February 2004)
Bouyer, P., et al.: Synthesis of Optimal Strategies Using HyTech. In: Proc. Games in Design and Verification GDV 2004. ENTCS, Elsevier, Amsterdam (2004)
Bouyer, P., Brinksma, E., Larsen, K.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)
Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Formal Methods in System Design 1(4), 385–415 (1992)
De Alfaro, L., Henzinger, T., Majumdar, R.: Symbolic algorithms for infinite-state games. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 536–550. Springer, Heidelberg (2001)
Henzinger, T.: The theory of hybrid automata. In: Proc. 11th IEEE Annual Symp. Logic in Computer Science LICS 1996, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)
Hune, T., Larsen, K., Pettersson, P.: Guided synthesis of control programs using uppaal. In: Proc. IEEE ICDS Int. Work. Distributed Systems Verification and Validation, pp. E15–E22. IEEE Computer Society Press, Los Alamitos (2000)
La Torre, S., Mukhopadhyay, S., Murano, A.: Optimal-reachability and control for acyclic weighted timed automata. In: Proc. 2nd IFIP Int. Conf. Theoretical Computer Science TCS 2002. IFIP Proceedings, vol. 223, pp. 485–497. Kluwer, Dordrecht (2002)
Larsen, K.: Resource-efficient scheduling for real time systems. In: Alur, R., Lee, I. (eds.) EMSOFT 2003. LNCS, vol. 2855, pp. 16–19. Springer, Heidelberg (2003)
Larsen, K., Behrmann, G., Brinksma, E., Fehnker, A., Hune, T., Pettersson, P., Romijn, J.: 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, pp. 493–505. Springer, Heidelberg (2001)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995)
Niebert, P., Tripakis, S., Yovine, S.: Minimum-time reachability for timed automata. In: Proc. 8th IEEE Mediterranean Conf. Control and Automation (2000)
Thomas, W.: On the synthesis of strategies in infinite games. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 1–13. Springer, Heidelberg (1995)
Wong-Toi, H.: The synthesis of controllers for linear hybrid automata. In: Proc. 36th IEEE Conf. Decision and Control, pp. 4607–4612. IEEE Computer Society Press, Los Alamitos (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G. (2004). Optimal Strategies in Priced Timed Game Automata. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-30538-5_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24058-7
Online ISBN: 978-3-540-30538-5
eBook Packages: Computer ScienceComputer Science (R0)