Interface Simulation Distances

TL;DR

This paper introduces a quantitative measure called interface simulation distance that extends classical interface refinement by allowing error tolerance, providing a metric for comparing system interfaces.

Contribution

It defines a new distance measure for interfaces, demonstrating its mathematical properties and applicability through case studies, advancing interface analysis techniques.

Findings

Interface simulation distance satisfies the triangle inequality.

Distance remains bounded under interface composition.

Case studies illustrate the framework's practical utility.

Abstract

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.