Abstract
In this paper, we present a method for computing the set of reachable states for networks consisting of the parallel composition of a finite number of the same hybrid automaton template with rectangular dynamics. The method utilizes a symmetric representation of the set of reachable states (modulo the automata indices) that we call anonymized states, which makes it scalable. Rather than explicitly enumerating each automaton index in formulas representing sets of states, the anonymized representation encodes only: (a) the classes of automata, which are the states of automata represented with formulas over symbolic indices, and (b) the number of automata in each of the classes. We present an algorithm for overapproximating the reachable states by computing state transitions in this anonymized representation. Unlike symmetry reduction techniques used in finite state models, the timed transition of a network composed of hybrid automata causes the continuous variables of all the automata to evolve simultaneously. The anonymized representation is amenable to both reducing the discrete and continuous complexity. We evaluate a prototype implementation of the representation and reachability algorithm in our satisfiability modulo theories (SMT)-based tool, Passel. Our experimental results are promising, and generally allow for scaling to networks composed of tens of automata, and in some instances, hundreds (or more) of automata.
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Basler, G., Mazzucchi, M., Wahl, T., Kroening, D.: Symbolic counter abstraction for concurrent software. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 64–78. Springer, Heidelberg (2009)
Behrmann, G., Bouyer, P., Fleury, E., Larsen, K.G.: Static guard analysis in timed automata verification. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 254–270. Springer, Heidelberg (2003)
Bengtsson, J., Larsen, K., Larsson, F., Pettersson, P., Yi, W.: UPPAAL: A tool suite for automatic verification of real-time systems. In: Alur, R., Sontag, E.D., Henzinger, T.A. (eds.) HS 1995. LNCS, vol. 1066, pp. 232–243. Springer, Heidelberg (1996)
Bogomolov, S., Herrera, C., Muñiz, M., Westphal, B., Podelski, A.: Quasi-dependent variables in hybrid automata. In: 17th International Conference on Hybrid Systems: Computation and Control (2014)
Braberman, V., Garbervetsky, D., Olivero, A.: Improving the verification of timed systems using influence information. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 21–36. Springer, Heidelberg (2002)
Clarke, E.M., Enders, R., Filkorn, T., Jha, S.: Exploiting symmetry in temporal logic model checking. Formal Methods in System Design 9, 77–104 (1996)
de Moura, L., Bjørner, N.S.: Z3: An efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)
Dill, D.L.: The murϕ verification system. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 390–393. Springer, Heidelberg (1996)
Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Formal Methods in System Design 9(1-2), 105–131 (1996)
Emerson, E., Wahl, T.: Dynamic symmetry reduction. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 382–396. Springer, Heidelberg (2005)
Hendriks, M., Behrmann, G., Larsen, K.G., Niebert, P., Vaandrager, F.W.: Adding symmetry reduction to UPPAAL. In: Larsen, K.G., Niebert, P. (eds.) FORMATS 2003. LNCS, vol. 2791, pp. 46–59. Springer, Heidelberg (2004)
Hendriks, M.: Model checking timed automata: Techniques and applications. Ph.D. thesis, University of Nijmegen, The Netherlands (2006)
Herrera, C., Westphal, B., Feo-Arenis, S., Muñiz, M., Podelski, A.: Reducing Quasi-Equal Clocks in Networks of Timed Automata. In: Jurdziński, M., Ničković, D. (eds.) FORMATS 2012. LNCS, vol. 7595, pp. 155–170. Springer, Heidelberg (2012)
Ip, C.N., Dill, D.L.: Better verification through symmetry. Formal Methods in System Design 9, 41–75 (1996)
Ip, C.N., Dill, D.L.: Verifying systems with replicated components in Murϕ. Formal Methods in System Design 14(3) (1999)
Johnson, T.T.: Uniform Verification of Safety for Parameterized Networks of Hybrid Automata. Ph.D. thesis, University of Illinois at Urbana-Champaign, Urbana, IL 61801 (2013)
Johnson, T.T., Mitra, S.: Parameterized verification of distributed cyber-physical systems: An aircraft landing protocol case study. In: ACM/IEEE 3rd International Conference on Cyber-Physical Systems (April 2012)
Johnson, T.T., Mitra, S.: A small model theorem for rectangular hybrid automata networks. In: Giese, H., Rosu, G. (eds.) FORTE 2012 and FMOODS 2012. LNCS, vol. 7273, pp. 18–34. Springer, Heidelberg (2012)
Johnson, T.T., Mitra, S.: Invariant synthesis for verification of parameterized cyber-physical systems with applications to aerospace systems. In: Proceedings of the AIAA Infotech at Aerospace Conference (AIAA Infotech 2013), Boston, MA (August 2013)
Obal, W.D., McQuinn, M., Sanders, W.: Detecting and exploiting symmetry in discrete-state Markov models. IEEE Transactions on Reliability 56(4), 643–654 (2007)
Si, Y., Sun, J., Liu, Y., Wang, T.: Improving model checking stateful timed csp with non-zenoness through clock-symmetry reduction. In: Groves, L., Sun, J. (eds.) ICFEM 2013. LNCS, vol. 8144, pp. 182–198. Springer, Heidelberg (2013)
Sun, J., Liu, Y., Dong, J.S., Liu, Y., Shi, L., André, E.: Modeling and verifying hierarchical real-time systems using stateful timed csp. ACM Trans. Softw. Eng. Methodol. 22(1), 1–29 (2013)
Sun, J., Liu, Y., Dong, J.S., Pang, J.: PAT: Towards flexible verification under fairness. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 709–714. Springer, Heidelberg (2009)
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Johnson, T.T., Mitra, S. (2014). Anonymized Reachability of Hybrid Automata Networks. In: Legay, A., Bozga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2014. Lecture Notes in Computer Science, vol 8711. Springer, Cham. https://doi.org/10.1007/978-3-319-10512-3_10
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DOI: https://doi.org/10.1007/978-3-319-10512-3_10
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