Static analysis by abstract interpretation of properties of imperfectly-clocked synchronous systems
The control units of embedded systems are often implemented as
synchronous systems, some being redundant so that they resist hardware failures.
In order to be realistic, we introduce a framework where these units
may be imperfectly-clocked and their communications non-instantaneous.
The semantics for such systems is defined as continuous-time boolean
signals, the control parts involving only few computations. The hardware
imperfections induce a huge number of possible behaviors so that the
specifications of such a system can only be proved by abstracting it.
We introduce several abstract domains and their interactions through
reductions that enable an automatic and abstract reasoning about the
high-level properties :
- stability and instability
- quantitative properties, i.e. integral or close notions
- qualitative comparison of behaviors at similar points of the system
(do they change their values at the same time ? Is this signal always
ahead of this other one ?)