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Stochastic Formal Methods for Hybrid Systems

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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Preprints, Working Papers, ...
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Contributor : Marc Daumas <>
Submitted on : Tuesday, February 24, 2009 - 1:14:50 PM
Last modification on : Monday, December 14, 2020 - 4:34:24 PM
Long-term archiving on: : Friday, September 24, 2010 - 12:17:28 PM


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  • HAL Id : hal-00107495, version 5
  • ARXIV : cs/0610110



Marc Daumas, David Lester, Erik Martin-Dorel, Annick Truffert. Stochastic Formal Methods for Hybrid Systems. 2009. ⟨hal-00107495v5⟩



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