Section: Overall Objectives


A cyber-physical (or reactive, or embedded) system is the integration of heterogeneous components originating from several design viewpoints: reactive software, some of which is embedded in hardware, interfaced with the physical environment through mechanical parts. Time takes different forms when observed from each of these viewpoints: it is discrete and event-based in software, discrete and time-triggered in hardware, continuous in mechanics or physics. Design of CPS often benefits from concepts of multiform and logical time(s) for their natural description. High-level formalisms used to model software, hardware and physics additionally alter this perception of time quite significantly.

In model-based system design, time is usually abstracted to serve the purpose of one of many design tasks: verification, simulation, profiling, performance analysis, scheduling analysis, parallelisation, distribution, or virtual prototyping. For example in non-real-time commodity software, timing abstraction such as number of instructions and algorithmic complexity is sufficient: software will run the same on different machines, except slower or faster. Alternatively, in cyber-physical systems, multiple recurring instances of meaningful events may create as many dedicated logical clocks, on which to ground modelling and design practices.

Time abstraction increases efficiency in event-driven simulation or execution (i.e SystemC simulation models try to abstract time, from cycle-accurate to approximate-time, and to loosely-time), while attempting to retain functionality, but without any actual guarantee of valid accuracy (responsibility is left to the model designer). Functional determinism (a.k.a. conflict-freeness in Petri Nets, monotonicity in Kahn PNs, confluence in Milner's CCS, latency-insensitivity and elasticity in circuit design) allows for reducing to some amount the problem to that of many schedules of a single self-timed behaviour, and time in many systems studies is partitioned into models of computation and communication (MoCCs). Multiple, multiform time(s) raises the question of combination, abstraction or refinement between distinct time bases. The question of combining continuous time with discrete logical time calls for proper discretisation in simulation and implementation. While timed reasoning takes multiple forms, there is no unified foundation to reasoning about multi-form time in system design.

The objective of project-team TEA is henceforth to define formal models for timed quantitative reasoning, or put simply for time reasoning, in embedded system design. Formal time models and calculi should allow us to revisit common domain problems in real-time system design, such as time predictability and determinism, memory ressources predictability, real-time scheduling, mixed-criticality and power management; yet from the perspective gained from inter-domain timed and quantitative abstraction or refinement relations. A regained focus on fundamentals will allow to deliver better tooled methodologies for virtual prototyping and integration of embedded architectures.