A randomized model for communicating embedded systems

Nowadays, there is an intense research activity in designing systems that operate in real life, physical environments. This research is spanned by various areas in computer science and engineering: embedded systems, reactive systems, wireless communications, hybrid systems, stochastic processes, etc. A severe limitation in the development of these systems is due to the mathematical foundation and complexity of the physical environment. Often, the physical environment is continuous and uncertain, and modelled in terms of continuous stochastic processes. These mathematics are quite different from the underlying mathematics of discrete controllers based on logic and algebra. In this paper, we make further developments of Hilbertean formal methods, an integrated specification framework based with a rich algebraic semantics. This framework axiomatises and abstracts away advanced structures from functional and stochastic analysis. We integrate a probabilistic version of Pi-calculus to provide a rigorous framework for embedded systems with mobile and adaptive communication structure. The integration mechanism is based on partial ordered sets. The resulting framework has the modelling power of connectionist models like neural networks. Moreover, we construct an energy integral to every specification. The power of formal specification and stochastic analysis are combined in a rigorous mathematical framework for the software development of embedded systems. In this way, we achieve a new foundation for the multidimensional codesign.