Abstract
Weighted timed automata extend timed automata with cost variables that can be used to model the evolution of various quantities. Although cost-optimal reachability is decidable (in polynomial space) on this model, it becomes undecidable on weighted timed games. This paper studies cost-optimal reachability problems on weighted timed automata and games under robust semantics. More precisely, we consider two perturbation game semantics that introduce imprecisions in the standard semantics, and bring robustness properties w.r.t. timing imprecisions to controllers. We give a polynomial-space algorithm for weighted timed automata, and prove the undecidability of cost-optimal reachability on weighted timed games, showing that the problem is robustly undecidable.
This work was partly supported by ANR project ImpRo (ANR-10-BLAN-0317), by ERC Starting grant EQualIS (308087) and by European project Cassting (FP7-ICT-601148).
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References
Alur, R., Bernadsky, M., Madhusudan, P.: Optimal reachability for weighted timed games. In: DÃaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 122–133. Springer, Heidelberg (2004)
Alur, R., Dill, D.L.: A theory of timed automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R., La Torre, S., Madhusudan, P.: Perturbed timed automata. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 70–85. Springer, Heidelberg (2005)
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)
Asarin, E., Bouajjani, A.: Perturbed Turing machines and hybrid systems. In: LICS 2001, pp. 269–278. IEEE Comp. Soc. Press (2001)
Asarin, E., Maler, O., Pnueli, A., Sifakis, J.: Controller synthesis for timed automata. In: SSC 1998, pp. 469–474. Elsevier Science (1998)
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)
Bouyer, P., Brihaye, T., Bruyère, V., Raskin, J.-F.: On the optimal reachability problem of weighted timed automata. Formal Methods in System Design 31(2), 135–175 (2007)
Bouyer, P., Brihaye, T., Markey, N.: Improved undecidability results on weighted timed automata. Information Processing Letters 98(5), 188–194 (2006)
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)
Bouyer, P., Markey, N., Sankur, O.: Robust reachability in timed automata: A game-based approach. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012, Part II. LNCS, vol. 7392, pp. 128–140. Springer, Heidelberg (2012)
Bouyer, P., Markey, N., Sankur, O.: Robust weighted timed automata and games. Research Report LSV-13-10, Laboratoire Spécification et Vérification, ENS Cachan, France, 25 p. (2013)
Brihaye, T., Bruyère, V., Raskin, J.-F.: On optimal timed strategies. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 49–64. Springer, Heidelberg (2005)
Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Information and Computation 208(6), 677–693 (2010)
Chatterjee, K., Henzinger, T.A., Prabhu, V.S.: Timed parity games: Complexity and robustness. Logicical Methods in Computer Science 7(4) (2011)
De Wulf, M., Doyen, L., Markey, N., Raskin, J.-F.: Robust safety of timed automata. Formal Methods in System Design 33(1-3), 45–84 (2008)
De Wulf, M., Doyen, L., Raskin, J.-F.: Almost ASAP semantics: From timed models to timed implementations. Formal Aspects of Computing 17(3), 319–341 (2005)
Fränzle, M.: Analysis of hybrid systems: An ounce of realism can save an infinity of states. In: Flum, J., RodrÃguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–140. Springer, Heidelberg (1999)
Gupta, V., Henzinger, T.A., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)
Henzinger, T.A., Raskin, J.-F.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)
Puri, A.: Dynamical properties of timed systems. Discrete Event Dynamic Systems 10(1-2), 87–113 (2000)
Sankur, O., Bouyer, P., Markey, N.: Shrinking timed automata. In: FSTTCS 2011. LIPIcs, vol. 13, pp. 375–386. Leibniz-Zentrum für Informatik (2011)
Sankur, O., Bouyer, P., Markey, N., Reynier, P.-A.: Robust controller synthesis in timed automata. In: Aires, B., D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013. LNCS, vol. 8052, pp. 546–560. Springer, Heidelberg (2013)
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Bouyer, P., Markey, N., Sankur, O. (2013). Robust Weighted Timed Automata and Games. In: Braberman, V., Fribourg, L. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2013. Lecture Notes in Computer Science, vol 8053. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40229-6_3
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DOI: https://doi.org/10.1007/978-3-642-40229-6_3
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