Abstract Interpretation of the Physical Inputs of Embedded Programs

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Abstract

We define an abstraction of the continuous variables that serve as inputs to embedded software. In existing static analyzers, these variables are most often abstracted by a constant interval, and this approach has shown its limits. We propose a different method that analyzes in a more precise way the continuous environment. This environment is first expressed as the semantics of a special continuous program, and we define a safe abstract semantics. We introduce the abstract domain of interval valued step functions and show that it safely over-approximates the set of continuous functions. The theory of guaranteed integration is then used to effectively compute an abstract semantics and we prove that this abstract semantics is safe.