Abstract
Specifications and implementations of complex physical systems tend to differ as low level effects such as sampling are often ignored when high level models are created. Thus, the low level models are often not exact refinements of the high level specification. However, they are similar to those. To bridge the gap between those models, we study robust simulation relations for hybrid systems. We identify a family of robust simulation relations that allow for certain bounded deviations in the behavior of a system specification and its implementation in both values of the system variables and timings. We show that for this relaxed version of simulation a broad class of logical properties is preserved. The question whether two systems are in simulation relation can be reduced to a reach avoid problem for hybrid games. We provide a sufficient condition under which a winning strategy for these games exists.
This work was partially supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS).
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References
Alur, R., Henzinger, T.A.: Logics and models of real time: A survey. In: Proceedings of the Real-Time: Theory in Practice, REX Workshop, London, UK, pp. 74–106. Springer, Heidelberg (1992)
Bouyer, P., Brihaye, T., Chevalier, F.: O-minimal hybrid reachability games. Logical Methods in Computer Science 6(1) (2009)
Damm, W., Dierks, H., Disch, S., Hagemann, W., Pigorsch, F., Scholl, C., Waldmann, U., Wirtz, B.: Exact and fully symbolic verification of linear hybrid automata with large discrete state spaces. Science of Computer Programming, Special Issue on Automated Verification of Critical Systems (to appear, 2011)
Damm, W., Dierks, H., Oehlerking, J., Pnueli, A.: Towards component based design of hybrid systems: Safety and stability. In: Manna, Z., Peled, D. (eds.) Time for Verification. LNCS, vol. 6200, pp. 96–143. Springer, Heidelberg (2010)
Davoren, J.M.: Epsilon-tubes and generalized skorokhod metrics for hybrid paths spaces. In: [17], pp. 135–149
Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010)
Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)
Frehse, G.: Phaver: algorithmic verification of hybrid systems past hytech. STTT 10(3), 263–279 (2008)
Frehse, G., Guernic, C.L., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: Spaceex: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)
Fränzle, M., Herde, C., Teige, T., Ratschan, S., Schubert, T.: Efficient solving of large non-linear arithmetic constraint systems with complex boolean structure. Journal on Satisfiability, Boolean Modeling and Computation 1, 209–236 (2007)
Girard, A., Julius, A.A., Pappas, G.J.: Approximate simulation relations for hybrid systems. Discrete Event Dynamic Systems 18(2), 163–179 (2008)
Girard, A., Pola, G., Tabuada, P.: Approximately bisimilar symbolic models for incrementally stable switched systems. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 201–214. Springer, Heidelberg (2008)
Henzinger, T.A.: The theory of hybrid automata. In: LICS, pp. 278–292. IEEE CS Press, Los Alamitos (1996)
Henzinger, T.A., Horowitz, B., Majumdar, R.: Rectangular hybrid games. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 320–335. Springer, Heidelberg (1999)
Henzinger, T.A., Majumdar, R., Prabhu, V.S.: Quantifying similarities between timed systems. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 226–241. Springer, Heidelberg (2005)
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Systems 2(4), 255–299 (1990)
Majumdar, R., Tabuada, P. (eds.): HSCC 2009. LNCS, vol. 5469. Springer, Heidelberg (2009)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems (an extended abstract). In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995)
Platzer, A., Quesel, J.D.: Keymaera: A hybrid theorem prover for hybrid systems (system description). In: Armando, A., Baumgartner, P., Dowek, G. (eds.) IJCAR 2008. LNCS (LNAI), vol. 5195, pp. 171–178. Springer, Heidelberg (2008)
Ratschan, S., She, Z.: Safety verification of hybrid systems by constraint propagation based abstraction refinement. ACM Journal in Embedded Computing Systems 6(1) (2007)
Stauner, T.: Discrete-time refinement of hybrid automata. In: Tomlin, C.J., Greenstreet, M.R. (eds.) HSCC 2002. LNCS, vol. 2289, pp. 407–420. Springer, Heidelberg (2002)
Thrane, C.R., Fahrenberg, U., Larsen, K.G.: Quantitative analysis of weighted transition systems. J. Log. Algebr. Program. 79(7), 689–703 (2010)
Tomlin, C., Lygeros, J., Sastry, S.: A Game Theoretic Approach to Controller Design for Hybrid Systems. Proceedings of IEEE 88, 949–969 (2000)
Vladimerou, V., Prabhakar, P., Viswanathan, M., Dullerud, G.E.: Stormed hybrid games. In: [17], pp. 480–484
Wulf, M.D., Doyen, L., Raskin, J.F.: Almost asap semantics: from timed models to timed implementations. Formal Asp. Comput. 17(3), 319–341 (2005)
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Quesel, JD., Fränzle, M., Damm, W. (2011). Crossing the Bridge between Similar Games. In: Fahrenberg, U., Tripakis, S. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2011. Lecture Notes in Computer Science, vol 6919. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24310-3_12
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