Interface Simulation Distances
This work addresses the need for more nuanced interface comparison in system design, offering a quantitative approach that is incremental over classical refinement methods.
The paper tackles the problem of quantifying behavioral differences between system component interfaces by introducing interface simulation distance, which extends the alternating refinement preorder to tolerate and count errors, and demonstrates its properties like triangle inequality and composition invariance through case studies.
The classical (boolean) notion of refinement for behavioral interfaces of system components is the alternating refinement preorder. In this paper, we define a distance for interfaces, called interface simulation distance. It makes the alternating refinement preorder quantitative by, intuitively, tolerating errors (while counting them) in the alternating simulation game. We show that the interface simulation distance satisfies the triangle inequality, that the distance between two interfaces does not increase under parallel composition with a third interface, and that the distance between two interfaces can be bounded from above and below by distances between abstractions of the two interfaces. We illustrate the framework, and the properties of the distances under composition of interfaces, with two case studies.