Linear Approximation of Continuous Systems with Trapezoid Step Functions

We introduce a novel abstract domain for the safe approximation of continuous functions in the context of abstract interpretation-based static analysis. The key-idea is to represent \(\mathcal{C}_+^2\) functions by a finite sequence of trapezoids. In this way, we get a strictly more precise approximation of the actual values with respect to existing approaches in the literature. Experimental results underline the effectiveness of the approach in terms of both precision and efficiency.

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