Abstract
Lazy linear hybrid automata (LLHA) model the discrete time behavior of control systems containing finite-precision sensors and actuators interacting with their environment under bounded inertial delays. In this paper, we present a symbolic technique for reachability analysis of lazy linear hybrid automata. The model permits invariants and guards to be nonlinear predicates but requires flow values to be constants. Assuming finite precision, flows represented by uniform linear predicates can be reduced to those containing values from a finite set of constants. We present an abstraction hierarchy for LLHA. Our verification technique is based on bounded model checking and k-induction for reachability analysis at different levels of the abstraction hierarchy within an abstraction-refinement framework. The counterexamples obtained during BMC are used to construct refinements in each iteration. Our technique is practical and compares favorably with state-of-the-art tools, as demonstrated on examples that include the Air Traffic Alert and Collision Avoidance System (TCAS).
Supported in part by SRC contract 1355.001, NSF grants CNS-0644436 & CNS-0627734, and Microsoft Research. The first author was also supported by the Berkeley Fellowship for Graduate Studies from UC Berkeley.
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References
Agrawal, M., Stephan, F., Thiagarajan, P.S., Yang, S.: Behavioural approximations for restricted linear differential hybrid automata. In: Hespanha, J.P., Tiwari, A. (eds.) HSCC 2006. LNCS, vol. 3927, pp. 4–18. Springer, Heidelberg (2006)
Agrawal, M., Thiagarajan, P.S.: Lazy rectangular hybrid automata. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 1–15. Springer, Heidelberg (2004)
Agrawal, M., Thiagarajan, P.S.: The discrete time behavior of lazy linear hybrid automata. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 55–69. Springer, Heidelberg (2005)
Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) Hybrid Systems. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1992)
Bryant, R.E., Kroening, D., Ouaknine, J., Seshia, S.A., Strichman, O., Brady, B.: Deciding bit-vector arithmetic with abstraction. In: Proceedings of TACAS 2007. LNCS, vol. 4424, pp. 358–372. Springer, Heidelberg (2007)
Chan, W., Anderson, R., Beame, P., Notkin, D.: Combining constraint solving and symbolic model checking for a class of a systems with non-linear constraints. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 316–327. Springer, Heidelberg (1997)
Clarke, E.M., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000)
Damm, W., Pinto, G., Ratschan, S.: Guaranteed termination in the verification of LTL properties of non-linear robust discrete time hybrid systems. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 99–113. Springer, Heidelberg (2005)
Deshpande, A., Godbole, D.N.A.G., Varaiya, P.: Design and evaluation tools for automated highway systems. In: Hybrid Systems, pp. 138–148 (1995)
Federal Aviation Administration. Introduction to TCAS II Version 7 (November 2000), http://www.arinc.com/downloads/tcas/tcas.pdf
Frehse, G.: PHAVer: Algorithmic verification of hybrid systems past HyTech. In: HSCC, pp. 258–273 (2005)
Henzinger, T.A., Kopke, P.W.: Discrete-time control for rectangular hybrid automata. TCS 221(1-2), 369–392 (1999)
Ho, P.-H.: Automatic analysis of hybrid systems. PhD thesis, Cornell Univ. (1995)
Jha, S.K., Krogh, B.H., Weimer, J., Clarke, E.M.: Reachability for Linear Hybrid Automata Using Iterative Relaxation Abstraction. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 287–300. Springer, Heidelberg (2007)
Livadas, C., Lygeros, J., Lynch, N.A.: High-level modeling and analysis of tcas. In: RTSS 1999, p. 115. IEEE Computer Society Press, Washington, DC, USA (1999)
Pappas, G., Tomlin, C., Sastry, S.: Conflict resolution for multi-agent hybrid systems. In: CDC, pp. 1184–1189 (1996)
Potocnik, B., Bemporad, A., Torrisi, F., Music, G., Zupancic, B.: Hysdel Modeling and Simulation of Hybrid Dynamical Systems. In: MATHMOD Conference, Vienna, Austria (February 2003)
Ratschan, S., She, Z.: Constraints for continuous reachability in the verification of hybrid systems. In: Calmet, J., Ida, T., Wang, D. (eds.) AISC 2006. LNCS (LNAI), vol. 4120, pp. 196–210. Springer, Heidelberg (2006)
TCAS201 Specification Datasheet. http://www.aeroflex.com/products/avionics/rf/datasheets/tcas201.pdf
Tiwari, A.: Approximate reachability for linear systems. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 514–525. Springer, Heidelberg (2003)
Tiwari, A., Khanna, G.: Series of abstractions for hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 465–478. Springer, Heidelberg (2002)
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Jha, S., Brady, B.A., Seshia, S.A. (2007). Symbolic Reachability Analysis of Lazy Linear Hybrid Automata. In: Raskin, JF., Thiagarajan, P.S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2007. Lecture Notes in Computer Science, vol 4763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75454-1_18
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