Towards composition of conformant systems

TL;DR

This paper explores conformance testing for Cyber-Physical Systems, introducing a framework that relates conformance measures to system composition, enabling the construction of complex systems from conformant components.

Contribution

It establishes a connection between conformance and approximate simulation relations for Open Metric Transition Systems, including a small-gain theorem for system interconnections.

Findings

Proved a small-gain theorem for OMTS.

Linked conformance with approximate simulation relations.

Enabled compositional reasoning for conformant systems.

Abstract

Motivated by the Model-Based Design process for Cyber-Physical Systems, we consider issues in conformance testing of systems. Conformance is a quantitative notion of similarity between the output trajectories of systems, which considers both temporal and spatial aspects of the outputs. Previous work developed algorithms for computing the conformance degree between two systems, and demonstrated how formal verification results for one system can be re-used for a system that is conformant to it. In this paper, we study the relation between conformance and a generalized approximate simulation relation for the class of Open Metric Transition Systems (OMTS). This allows us to prove a small-gain theorem for OMTS, which gives sufficient conditions under which the feedback interconnection of systems respects the conformance relation, thus allowing the building of more complex systems from conformant components.