Abstract
We consider the model checking problem of infinite state systems given in the form of parameterized discrete timed networks with multiple clocks. We show that this problem is decidable with respect to specifications given by B- or S-automata. Such specifications are very expressive (they strictly subsume \(\omega \)-regular specifications), and easily express complex liveness and safety properties. Our results are obtained by modeling the passage of time using symmetric broadcast, and by solving the model checking problem of parameterized systems of untimed processes communicating using k-wise rendezvous and symmetric broadcast. Our decidability proof makes use of automata theory, rational linear programming, and geometric reasoning for solving certain reachability questions in vector addition systems; we believe these proof techniques will be useful in solving related problems.
Benjamin Aminof and Florian Zuleger were supported by the Austrian National Research Network S11403-N23 (RiSE) of the Austrian Science Fund (FWF) and by the Vienna Science and Technology Fund (WWTF) through grant ICT12-059. Sasha Rubin is a Marie Curie fellow of the Istituto Nazionale di Alta Matematica.
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References
Abdulla, P.A., Deneux, J., Mahata, P.: Multi-clock timed networks. In: Ganzinger, H. (ed.) LICS, pp. 345–354, July 2004
Abdulla, P.A., Jonsson, B.: Model checking of systems with manyidentical timed processes. TCS 290(1), 241–264 (2003)
Alur, R.: Timed automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)
Aminof, B., Jacobs, S., Khalimov, A., Rubin, S.: Parameterized model checking of token-passing systems. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 262–281. Springer, Heidelberg (2014)
Aminof, B., Kotek, T., Rubin, S., Spegni, F., Veith, H.: Parameterized model checking of rendezvous systems. In: Baldan, P., Gorla, D. (eds.) CONCUR 2014. LNCS, vol. 8704, pp. 109–124. Springer, Heidelberg (2014)
Bojanczyk, M.: Beyond \(\omega \)-regular languages. In: STACS 2010, pp. 11–16 (2010)
Chevallier, R., Encrenaz-Tiphene, E., Fribourg, L., Xu, W.: Timed verification of the generic architecture of a memory circuit using parametric timed automata. Formal Methods in System Design 34(1), 59–81 (2009)
Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of ad hoc networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010)
Esparza, J., Finkel, A., Mayr, R.: On the verification of broadcast protocols. In: LICS, pp. 352–359 (1999)
Esparza, J., Nielsen, M.: Decidability issues for petri nets - a survey. Bulletin of the EATCS 52, 244–262 (1994)
German, S.M., Sistla, A.P.: Reasoning about systems with many processes. JACM 39(3), 675–735 (1992)
Kouvaros, P., Lomuscio, A.: A cutoff technique for the verification of parameterised interpreted systems with parameterised environments. In: IJCAI 2013 (2013)
Spalazzi, L., Spegni, F.: Parameterized model-checking of timed systems with conjunctive guards. In: Giannakopoulou, D., Kroening, D. (eds.) VSTTE 2014. LNCS, vol. 8471, pp. 235–251. Springer, Heidelberg (2014)
Suzuki, I.: Proving properties of a ring of finite-state machines. Inf. Process. Lett. 28(4), 213–214 (1988)
Vardi, M.Y.: An automata-theoretic approach to linear temporallogic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)
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Aminof, B., Rubin, S., Zuleger, F., Spegni, F. (2015). Liveness of Parameterized Timed Networks. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_30
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DOI: https://doi.org/10.1007/978-3-662-47666-6_30
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