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 call for unambiguous design models based on models and methods to translate a high-level system specification into a distribution of purely sequential programs together with semantics-preserving transformations and high-level optimizations such as hierarchization (sequentialization) or desynchronization (protocol synthesis).

System design based on the so-called “synchronous hypothesis” has in this respect focused the attention of many academic and industrial actors. The synchronous paradigm abstracts the non-functional implementation details of a system and focuses on the logics behind the instants at which the system functionalities should be secured.

Synchronous design models and languages provide intuitive models for embedded systems that ease the generation of systems and architectures and the verification of their functionalities [1] .

In the relational mathematical model behind the design language Signal, the supportive dataflow 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 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.