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Static Analysis by Abstract Interpretation of Hybrid Systems

In this article, we introduce a new way of modelling and analyzing hybrid systems. Our model insists on a clear separation between the discrete and continuous worlds, making it possible to use with little effort existing programs. The analysis, based on abstract interpretation, can prove safety properties concerning the use of floating point numbers instead of real numbers in hybrid systems. For this analysis, we developed a new domain, the domain of step-wise functions. Our abstraction consist of an abstraction of time in order to make the environments representable and of an abstraction of the continuous functions to make them computable.