Section: Scientific Foundations

Introduction

Embedded systems are not new, but their pervasive introduction in ordinary-life objects (cars, telephone, home appliances) brought a new focus onto design methods for such systems. New development techniques are needed to meet the challenges of productivity in a competitive environment. Synchronous languages rely on the synchronous hypothesis, which lets computations and behaviors be divided into a discrete sequence of computation steps which are equivalently called reactions or execution instants. In itself this assumption is rather common in practical embedded system design.

But the synchronous hypothesis adds to this the fact that, inside each instant, the behavioral propagation is well-behaved (causal), so that the status of every signal or variable is established and defined prior to being tested or used. This criterion, which may be seen at first as an isolated technical requirement, is in fact the key point of the approach. It ensures strong semantic soundness by allowing universally recognized mathematical models to be used as supporting foundations. In turn, these models give access to a large corpus of efficient optimization, compilation, and formal verification techniques. The synchronous hypothesis also guarantees full equivalence between various levels of representation, thereby avoiding altogether the pitfalls of non-synthesizability of other similar formalisms. In that sense the synchronous hypothesis is, in our view, a major contribution to the goal of model-based design of embedded systems.

We shall describe the synchronous hypothesis and its mathematical background, together with a range of design techniques enpowered by the approach. Declarative formalisms implementing the synchronous hypothesis can be cast into a model of computation [8] consisting of a domain of traces or behaviors and of semi-lattice structure that renders the synchronous hypothesis using a timing equivalence relation: clock equivalence. Asynchrony [32] can be superimposed on this model by considering a flow equivalence relation as well as heterogeneous systems  [33] by parameterizing composition with arbitrary timing relations.