Bisimulation, Logic and Mobility for Markovian Systems

Nowadays, anyone can easily observe an explosive development in distributed em- bedded systems like sensor networks, gene regulatory networks and other system biology areas. A general tendency in this development is the integration of di er- ent features, like mobility, randomness, continuity and discrete/continuous mixed behaviors. In this paper, we present two formal mechanisms for developing a for- mal framework, in which these various features can be investigated altogether. One mechanism represents a unifying axiomatization of deterministic and stochastic au- tomata, in the spirit of the recently introduced paradigm called Hilbertian formal methods [6]. The second one proposes a generic technique based on the categorical domain theory for adding new features to an existing model. This mechanism consti- tutes a formal approach to a recent development paradigm called multi-dimensional codesign [5]. In the limited space of this paper, we restrict our presentation to a class of systems that mix continuous evolutions with logical mobility.