Composing Heterogeneous Reactive Systems

We present a compositional theory of heterogeneous reactive systems. The approach is based on the concept of tags marking the events of the signals of a system. Tags can be used for multiple purposes from indexing evolution in time (time stamping) to expressing relations among signals like coordination (e.g., synchrony and asynchrony), and causal dependencies. The theory provides flexibility in system modeling because it can be used both as a unifying mathematical framework to relate heterogeneous models of computations and as a formal vehicle to implement complex systems by combining heterogeneous components. In particular, we introduce an algebra of tag structures to define heterogeneous parallel composition formally. Morphisms between tag structures are used to define relationships between heterogeneous models at different levels of abstraction. In particular, they can be used to represent design transformations from tightly-synchronized specifications to loosely-synchronized implementations. The theory has an important application in the correct-by-construction deployment of synchronous design on distributed architectures.

Keywords : reactive systems, embedded systems, synchronous, asynchronous, GALS, formal methods, heterogeneous systems.