Quantifying the Precision of Numerical Abstract Domains

In the context of the Abstract Interpretation framework, initiated by Cousot and Cousot to model program static analyses, numerous numerical abstract domains have been proposed. Their number is due to both the intended usage of the domains (properties to prove) and the trade-off between precision and computation efficiency. In this paper, we propose a way to quantify the precision of abstract values belonging to numerical domains like intervals, octagons or polyhedra. To do so, we rely on the fact that abstract values of that kind describe some volumes that can be measured. The article focuses on the definition and computation of this precision, also providing examples of application