Quantifying Similarities Between Timed Systems
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.
Unable to display preview. Download preview PDF.
- 6.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)Google Scholar
- 17.Gupta, V., Jagadeesan, R., Panangaden, P.: Approximate reasoning for real-time probabilistic processes. In: QEST 2004, pp. 304–313. IEEE, Los Alamitos (2004)Google Scholar
- 19.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)Google Scholar
- 20.Huang, J., Voeten, J., Geilen, M.: Real-time property preservation in concurrent real-time systems. In: RTCSA 2004. Springer, Heidelberg (2004)Google Scholar
- 22.Tasiran, S.: Compositional and Hierarchical Techniques for the Formal Verification of Real-Time Systems. Dissertation, UC Berkeley (1998)Google Scholar