Section: New Results

Extensions of the Signal language and the Polychrony formal model

Participants : Thierry Gautier, Paul Le Guernic.

The different works related to the use of the polychronous model as semantic median model (which has also a syntactic instance) for different effective models (AADL [15] , Simulink via GeneAuto, UML via CCSL...) lead us to study various possible extensions of the semantic model as well as the syntactic one.

Thus, we are defining a new version, V5, of Signal, that will be a deep evolution from the current V4 version.

In particular, we are investigating the way state diagrams are best represented in the polychronous model of computation, maintaining the multi-clock characteristic property of the representation. We propose a semantic model for these automata, that relies on the Boolean algebra of clocks. A special case of automata is those that may be represented as regular clock expressions, for which we develop a specific formal calculus. These regular expressions may be used as a powerful manner to express regular dynamic properties of polychronous processes. In correspondence with these models, we are defining syntactic structures to represent these Signal State Diagrams.

Moreover, an important challenge we want to address in the next few years is that of providing design automation techniques and tools for engineering heterogeneous cyber-physical systems (CPS). This leads in particular to new requirements related to the language itself in which we want to describe such software architectures. With respect to the current V4 version of Signal, the basic idea is to extend Signal with a syntactic structure that encapsulates a polychronous process $P$ in a system, $S$, that could have a continuous temporal domain providing a real-time clock presented in some time unit (fs, ..., ms, ..., sec, mn, ...). Such a real-time clock can be used as a usual signal in the process $P$ encapsulated in $S$. Systems $S_1$, ..., $S_n$ may be composed (with the standard composition of Signal) in a same system $S$, but the ms of a given system $S_i$ is a priori not synchronous with the ms of another system $S_j$. Then it is possible to specify constraints in the system $S$ on these different signals, to express for instance some variation limits of different clocks.

For that purpose, we have defined a new taxonomy of polychronous processes to characterize precisely the following classes: system, task, (logical) process, function, reaction, diagram, observer, controller... This characterization is based on properties such as time reference, input-output clock relations, input-output dependences, determinism, exo/endochrony. For example, a system is either a physical system abstraction, or a basic system, or a system of systems. A basic system has a unique continuous time reference; it provides an internal actual discrete time unit subset of its external continuous time, shared by all its components. As another example, for a subclass of logical processes: a function is a deterministic, inout clocked, endochronous and atomic process that denotes a mathematical flow function. All these different semantic classes are provided syntactic counterparts in the new Signal V5.