Abstract
Linear duration invariants (LDIs) are important safety properties of real-time systems. In this paper, we reduce the problem of verification of a network of timed automata against an LDI to an equivalent problem of model checking whether a failure state is never reached. Our approach is first to transform each component automaton \({\mathcal A}_i\) of the network \({\mathcal A}\) to an automaton \({\mathcal G}\). The transformation helps us to record entry and exit to critical locations that appear in the LDI. We then introduce an auxiliary checker automaton \({\mathcal S}\) and define a failure state to verify the LDI on a given interval. Since a model checker checks exhaustively, a failure of the checker automaton to find the failure state will prove that the LDI holds.
The work is partly supported by the projects NSFC-60603037, NSFC-90718014, NSFC-60721061, NSFC-60573007, NSFC-90718041, NSFC-60736017, STCSM No.08510700300, and HighQSoftD and HTTS funded by Macao S&TD Fund.
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References
Alur, R., Dill, D.L.: A Theory of Timed Automata. Theoretical Computer Science 126(2), 183–235 (1994)
Alur, R.: Timed Automata. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 8–22. Springer, Heidelberg (1999)
Braberman, V.A., Van Hung, D.: On Checking Timed Automata for Linear Duration Invariants. In: Proc. RTSS 1998, pp. 264–273. IEEE Computer Society Press, Los Alamitos (1998)
Emerson, E.A., Halpern, J.Y.: “Sometimes” and “Not Never” Revisited: On Branching versus Linear Time Temporal Logic. Journal of the ACM 33(1), 151–178 (1986)
Henzinger, T., Manna, Z., Pnueli, A.: What Good Are Digital Clocks? In: Kuich, W. (ed.) ICALP 1992. LNCS, vol. 623, pp. 545–558. Springer, Heidelberg (1992)
Chakravorty, G., Pandya, P.K.: Digitizing Interval Duration Logic. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 167–179. Springer, Heidelberg (2003)
Bosnacki, D.: Digitization of Timed Automata. In: Proc. FMICS 1999, pp. 283–302 (1999)
Van Hung, D., Giang, P.H.: Sampling Semantics of Duration Calculus. In: Jonsson, B., Parrow, J. (eds.) FTRTFT 1996. LNCS, vol. 1135, pp. 188–207. Springer, Heidelberg (1996)
Franzle, M.: Model-Checking Dense-Time Duration Calculus. Formal Asp. Comput. 16(2), 121–139 (2004)
Li, X., Van Hung, D.: Checking Linear Duration Invariants by Linear Programming. In: Jaffar, J., Yap, R.H.C. (eds.) ASIAN 1996. LNCS, vol. 1179, pp. 321–332. Springer, Heidelberg (1996)
Thai, P.H., Van Hung, D.: Verifying Linear Duration Constraints of Timed Automata. In: Liu, Z., Araki, K. (eds.) ICTAC 2004. LNCS, vol. 3407, pp. 295–309. Springer, Heidelberg (2005)
Chaochen, Z., Hoare, C.A.R., Ravn, A.P.: A Calculus of Durations. Information Processing Letters 40(5), 269–276 (1991)
Zhou, C., Zhang, J., Yang, L., Li, X.: Linear Duration Invariants. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 86–109. Springer, Heidelberg (1994)
Zhou, C., Hansen, M.R.: Duration Calculus. A Formal Approach to Real-Time Systems (2004)
Behrmann, G., David, A., Larsen, K.G.: A Tutorial on Uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)
Zhang, M., Van Hung, D., Liu, Z.: Verification of Linear Duration Invariants by Model Checking CTL Properties. In: Fitzgerald, J.S., Haxthausen, A.E., Yenigun, H. (eds.) ICTAC 2008. LNCS, vol. 5160, pp. 395–409. Springer, Heidelberg (2008)
Pandya, P.K.: Interval Duration Logic: Expressiveness and Decidability. ENTCS 65(6) (2002)
Meyer, R., Faber, J., Rybalchenko, A.: Model Checking Duration Calculus: A Practical Approach. In: Barkaoui, K., Cavalcanti, A., Cerone, A. (eds.) ICTAC 2006. LNCS, vol. 4281, pp. 332–346. Springer, Heidelberg (2006)
Fränzle, M., Hansen, M.R.: Deciding an Interval Logic with Accumulated Durations. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 201–215. Springer, Heidelberg (2007)
Liu, Z., Joseph, M.: Specification and Verification of Fault-Tolerance, Timing, and Scheduling. ACM Trans. Program. Lang. Syst. 21(1), 46–89 (1999)
Zhou, C., Hansen, M.R., Ravn, A.P., Rischel, H.: Duration Specifications for Shared Processors. In: Vytopil, J. (ed.) FTRTFT 1992. LNCS, vol. 571, pp. 21–32. Springer, Heidelberg (1991)
Zheng, Y., Zhou, C.: A Formal Proof of the Deadline Driven Scheduler. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 756–775. Springer, Heidelberg (1994)
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Zhang, M., Liu, Z., Zhan, N. (2010). Model Checking Linear Duration Invariants of Networks of Automata. In: Arbab, F., Sirjani, M. (eds) Fundamentals of Software Engineering. FSEN 2009. Lecture Notes in Computer Science, vol 5961. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11623-0_14
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DOI: https://doi.org/10.1007/978-3-642-11623-0_14
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