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Stochastic Formal Methods for Hybrid Systems

Marc Daumas·David Lester·Erik Martin-Dorel·Annick Truffert
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Abstract

We provide a framework to bound the probability that accumulated errors were never above a given threshold on hybrid systems. Such systems are used for example to model an aircraft or a nuclear power plant on one side and its software on the other side. This report contains simple formulas based on Lévy's and Markov's inequalities and it presents a formal theory of random variables with a special focus on producing concrete results. We selected four very common applications that fit in our framework and cover the common practices of hybrid systems that evolve for a long time. We compute the number of bits that remain continuously significant in the first two applications with a probability of failure around one against a billion, where worst case analysis considers that no significant bit remains. We are using PVS as such formal tools force explicit statement of all hypotheses and prevent incorrect uses of theorems.

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Marc Daumas, David Lester, Erik Martin-Dorel, Annick Truffert. 2009-02-24. Stochastic Formal Methods for Hybrid Systems. https://arxiv.org/abs/cs/0610110

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