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.
Type de document :
Pré-publication, Document de travail
2009
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https://hal.archives-ouvertes.fr/hal-00107495
Contributeur : Marc Daumas <>
Soumis le : mardi 24 février 2009 - 13:14:50
Dernière modification le : jeudi 9 avril 2015 - 15:37:04
Document(s) archivé(s) le : vendredi 24 septembre 2010 - 12:17:28

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

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

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