An integrated specification framework for embedded systems

In this paper, we address the complex issue of representation of continuous behaviour of the environment of the embedded controllers. In our approach, we propose two novel ideas. One is to consider the weak solutions to describe the evolution of the dynamical systems. The second novelty is to make available, at the design stage, the information about concurrent evolutions of the environment. We propose a new logic called the Hilbertian logic for representing continuous behaviours. Then, we use the causal order relations to integrate this logic with a probabilistic process algebra. For the resulting specification framework, we construct a denotational semantics rich in mathematical properties. Keywords: embedded systems, causal order relations, weak solutions, probabilistic process algebra.