Abstract
We address the problem of computing the infimum accumulated weight for the reachability of some goal location in weighted timed automata. While there already exist efficient techniques to solve this problem, we propose here a backwards symbolic algorithm computing the accumulated weight to the goal, instead of the accumulated weight from the initial state. Going backwards has in itself a few advantages: most notably it does not require any extrapolation operation to ensure termination. Also it may be more efficient than going forward if the set of co-reachable states is smaller than the set of reachable states. Backwards algorithms are also instrumental in several problems beyond reachability, like control problems for instance. We obtain our backward algorithm by proposing extensions of the classical action and time predecessor operations on zones to account for weights. We have implemented the approach and report on its performance.
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References
Alur, R., Dill, D.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 49–62. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45351-2_8
Behrmann, G., et al.: Minimum-cost reachability for priced time automata. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 147–161. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45351-2_15
Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Optimal scheduling using priced timed automata. SIGMETRICS Perform. Eval. Rev. 32(4), 34–40 (2005)
Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: The expressive power of time Petri nets. Theor. Comput. Sci. 474, 1–20 (2013)
Berendsen, J., Jansen, D.N., Katoen, J.: Probably on time and within budget: on reachability in priced probabilistic timed automata. In: 3rd International Conference on the Quantitative Evaluation of Systems (QEST 2006), pp. 311–322. IEEE Computer Society, Riverside (September 2006)
Berendsen, J., Jansen, D.N., Vaandrager, F.W.: Fortuna: model checking priced probabilistic timed automata. In: 7th International Conference on the Quantitative Evaluation of Systems (QEST 2010), pp. 273–281. IEEE Computer Society, Williamsburg (September 2010)
Boucheneb, H., Lime, D., Parquier, B., Roux, O.H., Seidner, C.: Optimal reachability in cost time Petri nets. In: Abate, A., Geeraerts, G. (eds.) FORMATS 2017. LNCS, vol. 10419, pp. 58–73. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-65765-3_4
Bouyer, P.: Untameable timed automata!. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36494-3_54
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). https://doi.org/10.1007/978-3-540-30538-5_13
Bouyer, P., Colange, M., Markey, N.: Symbolic optimal reachability in weighted timed automata. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 513–530. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41528-4_28
Bouyer, P., Laroussinie, F.: Model checking timed automata. In: Modeling and Verification of Real-time Systems, pp. 111–140. ISTE - Wiley (2008)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005). https://doi.org/10.1007/11539452_9
Enevoldsen, S., Guldstrand Larsen, K., Srba, J.: Abstract dependency graphs and their application to model checking. In: Vojnar, T., Zhang, L. (eds.) TACAS 2019. LNCS, vol. 11427, pp. 316–333. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-17462-0_18
Gardey, G., Roux, O.H., Roux, O.F.: State space computation and analysis of time Petri nets. Theory Pract. Logic Program. (TPLP) 6(3), 301–320 (2006). Special Issue on Specification Analysis and Verification of Reactive Systems
Herbreteau, F., Srivathsan, B., Walukiewicz, I.: Better abstractions for timed automata. Inf. Comput. 251, 67–90 (2016)
Larsen, K., et al.: As cheap as possible: effcient 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). https://doi.org/10.1007/3-540-44585-4_47
Larsen, K.G., Pettersson, P., Yi, W.: Model-checking for real-time systems. In: Reichel, H. (ed.) FCT 1995. LNCS, vol. 965, pp. 62–88. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-60249-6_41
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. J. Softw. Tools Technol. Transf. (STTT) 1(1–2), 134–152 (1997)
Lime, D., Roux, O.H., Seidner, C., Traonouez, L.-M.: Romeo: a parametric model-checker for Petri nets with stopwatches. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 54–57. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-00768-2_6
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). https://doi.org/10.1007/3-540-59042-0_76
Rasmussen, J.I., Larsen, K.G., 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). https://doi.org/10.1007/978-3-540-24730-2_19
Rasmussen, J.I., Larsen, K.G., Subramani, K.: On using priced timed automata to achieve optimal scheduling. Form. Methods Syst. Des. 29(1), 97–114 (2006)
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Parrot, R., Lime, D. (2020). Backward Symbolic Optimal Reachability in Weighted Timed Automata. In: Bertrand, N., Jansen, N. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2020. Lecture Notes in Computer Science(), vol 12288. Springer, Cham. https://doi.org/10.1007/978-3-030-57628-8_3
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