## Section: Overall Objectives

### The polychronous approach

Despite overwhelming advances in embedded systems design, existing techniques and tools merely provide *ad-hoc* solutions to the challenging issue of the productivity gap. The pressing demand for design tools has sometimes hidden the need to lay mathematical foundations below design languages. Many illustrating examples can be found, e.g. the variety of very different formal semantics found in state-diagram formalisms. Even though these design languages benefit from decades of programming practice, they still give rise to some diverging interpretations of their semantics.

The need for higher abstraction-levels and the rise of stronger market constraints now make the need for unambiguous design models more obvious. This challenge requires models and methods to translate a high-level system specification into a distribution of purely sequential programs and to implement semantics-preserving transformations and high-level optimizations such as hierarchization (sequentialization) or desynchronization (protocol synthesis).

In this aim, system design based on the so-called ``synchronous hypothesis'' has focused the attention of many academic and industrial actors. The synchronous paradigm consists of abstracting the non-functional implementation details of a system and lets one benefit from a focused reasoning on the logics behind the instants at which the system functionalities should be secured.

With this point of view, synchronous design models and languages provide intuitive models for embedded systems [4] . This affinity explains the ease of generating systems and architectures and verify their functionalities using compilers and related tools that implement this approach.

In the relational mathematical model behind the design language Signal, the supportive data-flow notation of Polychrony, this affinity goes beyond the domain of purely sequential systems and synchronous circuits and embraces the context of complex architectures consisting of synchronous circuits and desynchronization protocols: globally asynchronous and locally synchronous architectures (GALS).

This unique feature is obtained thanks to the fundamental notion of *polychrony* : the capability to describe systems in which components obey to multiple clock rates. It provides a mathematical foundation to a notion of *refinement* : the ability to model a system from the early stages of its requirement specifications (relations, properties) to the late stages of its synthesis and deployment (functions, automata).

The notion of polychrony goes beyond the usual scope of a programming language, allowing for specifications and properties to be described. As a result, the Signal design methodology draws a continuum from synchrony to asynchrony, from specification to implementation, from abstraction to refinement, from interface to implementation. Signal gives the opportunity to seamlessly model embedded systems at multiple levels of abstraction while reasoning within a simple and formally defined mathematical model.

The inherent flexibility of the abstract notion of signal handled in Signal invites and favors the design of correct-by-construction systems by means of well-defined model transformations that preserve the intended semantics and stated properties of the architecture under design.