Abstract
We define quantitative similarity functions between timed transition systems that measure the degree of closeness of two systems as a real, in contrast to the traditional boolean yes/no approach to timed simulation and language inclusion. Two systems are close if for each timed trace of one system, there exists a corresponding timed trace in the other system with the same sequence of events and closely corresponding event timings. We show that timed CTL is robust with respect to our quantitative version of bisimilarity, in particular, if a system satisfies a formula, then every close system satisfies a close formula. We also define a discounted version of CTL over timed systems, which assigns to every CTL formula a real value that is obtained by discounting real time. We prove the robustness of discounted CTL by establishing that close states in the bisimilarity metric have close values for all discounted CTL formulas.
This research was supported in part by the AFOSR MURI grant F49620-00-1-0327 and the NSF grants CCR-0208875, CCR-0225610, and CCR-0427202.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alur, R., Courcoubetis, C., Dill, D.L.: Model checking in dense real time. Inf. and Comp. 104, 2–34 (1993)
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994)
Alur, R., La Torre, S., Madhusudan, P.: Perturbed timed automata. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 70–85. Springer, Heidelberg (2005)
Bouyer, P., Brinksma, E., Larsen, K.G.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)
Caspi, P., Benveniste, A.: Toward an approximation theory for computerised control. In: Sangiovanni-Vincentelli, A.L., Sifakis, J. (eds.) EMSOFT 2002. LNCS, vol. 2491, pp. 294–304. Springer, Heidelberg (2002)
Cerans, K.: Decidability of bisimulation equivalences for parallel timer processes. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 302–315. Springer, Heidelberg (1993)
Clarke, E.M., Emerson, E.A., Sistla, A.P.: Automatic verification of finite-state concurrent systems using temporal logic specifications. ACM Trans. Program. Lang. Syst. 8, 244–263 (1986)
Comon, H., Jurski, Y.: Timed automata and the theory of real numbers. In: Baeten, J.C.M., Mauw, S. (eds.) CONCUR 1999. LNCS, vol. 1664, pp. 242–257. Springer, Heidelberg (1999)
Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. Formal Methods in System Design 1, 385–415 (1992)
de Alfaro, L., Faella, M., Henzinger, T.A., Majumdar, R., Stoelinga, M.: Model checking discounted temporal properties. In: Jensen, K., Podelski, A. (eds.) TACAS 2004. LNCS, vol. 2988, pp. 77–92. Springer, Heidelberg (2004)
de Alfaro, L., Faella, M., Stoelinga, M.: Linear and branching metrics for quantitative transition systems. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 97–109. Springer, Heidelberg (2004)
de Alfaro, L., Henzinger, T.A., Majumdar, R.: Discounting the future in systems theory. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 1022–1037. Springer, Heidelberg (2003)
De Wulf, M., Doyen, L., Markey, N., Raskin, J.-F.: Robustness and implementability of timed automata. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 118–133. Springer, Heidelberg (2004)
Desharnais, J., Gupta, V., Jagadeesan, R., Panangaden, P.: Metrics for labeled Markov processes. Theor. Comput. Sci. 318, 323–354 (2004)
Fränzle, M.: Analysis of hybrid systems: An ounce of realism can save an infinity of states. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 126–140. Springer, Heidelberg (1999)
Gupta, V., Henzinger, T.A., Jagadeesan, R.: Robust timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 331–345. Springer, Heidelberg (1997)
Gupta, V., Jagadeesan, R., Panangaden, P.: Approximate reasoning for real-time probabilistic processes. In: QEST 2004, pp. 304–313. IEEE, Los Alamitos (2004)
Henzinger, T.A., Raskin, J.-F.: Robust undecidability of timed and hybrid systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 145–159. Springer, Heidelberg (2000)
Huang, J., Voeten, J., Geilen, M.: Real-time property preservation in approximations of timed systems. In: MEMOCODE 2003, pp. 163–171. IEEE, Los Alamitos (2003)
Huang, J., Voeten, J., Geilen, M.: Real-time property preservation in concurrent real-time systems. In: RTCSA 2004. Springer, Heidelberg (2004)
Puri, A.: Dynamical properties of timed automata. In: Ravn, A.P., Rischel, H. (eds.) FTRTFT 1998. LNCS, vol. 1486, pp. 210–227. Springer, Heidelberg (1998)
Tasiran, S.: Compositional and Hierarchical Techniques for the Formal Verification of Real-Time Systems. Dissertation, UC Berkeley (1998)
De Wulf, M., Doyen, L., Raskin, J.-F.: Almost ASAP semantics: From timed models to timed implementations. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 296–310. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Henzinger, T.A., Majumdar, R., Prabhu, V.S. (2005). Quantifying Similarities Between Timed Systems. In: Pettersson, P., Yi, W. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2005. Lecture Notes in Computer Science, vol 3829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11603009_18
Download citation
DOI: https://doi.org/10.1007/11603009_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-30946-8
Online ISBN: 978-3-540-31616-9
eBook Packages: Computer ScienceComputer Science (R0)