1 / 124 3 / 124 Model checking int-02 requirements (safety, liveness) specification, e.g., temporal formula Φ Φ Φ reactive system abstract model M M M model checking "does M |= Φ M |= Φ M |= Φ hold ?" no yes 4 / 124 Probabilistic model checking int-03 quantitative requirements specification, e.g., temporal formula Φ Φ Φ probabilistic reactive system probabilistic model M M M probabilistic model checking probability for "bad behaviors" is < 10 −6 < 10 −6 < 10 −6 probability for "good behaviors"

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... s 1 1 1 expected costs for .... / 124 Probabilistic model checking int-03 quantitative requirements linear temporal formula Φ Φ Φ (path event) probabilistic reactive system Markov decision process M M M probabilistic model checking quantitative analysis of M M M against Φ Φ Φ probability for "bad behaviors" is < 10 −6 < 10 −6 < 10 −6 probability for "good behaviors" is 1 1 1 6 / 124 Outline overview • Markov decision processes (MDP) and quantitative analysis against path events • partial order reduction for MDP • partially-oberservable MDP • conclusions 7 / 124