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Extra resources for ARRL/CRRL Amateur Radio 9th Computer Networking Conference, London, Ontario Cana
T =⇒ t ∧ (s , t ) ∈ R – s −→ s ⇒ ∃ t . t =⇒ t ∧ (s , t ) ∈ R ε(X) ε(X) – s −→ s ∧ t −→ t ∧ s [X] = t [X] ⇒ (s , t ) ∈ R a a – t −→ ∧ a ∈ Au ⇒ s −→ We lift the notion of timed ready simulation to timed automata just as we did for timed simulation. We now state our wanted theorem saying that is indeed a precongruence and hence supports compositional reasoning. Theorem 2. Let A C and B D be timed automata compositions such that IWB D ⊆ IWA C . Also, assume that B and D are both τ -free. If, 1. A B and C D, and 2.
1 Next, the o-minimal hybrid automata of  are extended to the probabilistic context. 7 of , except for the following alterations: naturally, we dispense with the notion of edges connecting control modes, and replace them with a set of distributions; also, for every v ∈ V and all µ ∈ prob(v), the sets inv (v) and pre v (µ) are semi-algebraic with rational coeﬃcients, and, for every (w, post, X) ∈ support(µ), the set post is semi-algebraic with rational coeﬃcients and X = X . Finally, to obtain probabilistic o-minimal hybrid automata, we assume that the initial point of the model is unique.
Johan Bengtsson, David Griffioen, K˚ are Kristoffersen, Kim G. Larsen, Fredrik Larsson, Paul Pettersson, and Wang Yi. Verification of an Audio Protocol with Bus Collision Using Uppaal. In Proceedings of CAV’96, volume 1102 of Lecture Notes in Computer Science. Springer Verlag, 1996. 8. D. Dams. Abstract Interpretation and Partition Refinement for Model Checking. PhD thesis, Eindhoven University of Technology, 1996. 9. C. Daws, A. Olivero, S. Tripakis, and S. Yovine. The tool kronos. In Hybrid Systems III, Verification and Control, volume 1066 of Lecture Notes in Computer Science.