Towards a Formal Framework for Multidimensional Codesign

Multidimensional codesign is a recently proposed paradigm for integrating different system dimensions in sensor networks. Examples of such dimensions are logical and physical mobility, continuous and discrete transitions, deterministic and random evolutions and features resulting from their interaction, like deterministic and stochastic hybrid behaviours. In this paper, we propose a unifying computational model that considers multiple dimensions, inspired by the Hilbertian Formal Methods paradigm. We couple this model with an integration framework based on domain theory. In this framework new dimensions can be incrementally added, and we illustrate this technique by adding logical mobility to the computational model. The new model has a very promising modelling power, offering all formal ingredients of a neural network. We further investigate bisimulation for systems mixing physical and logical mobility. We identify and solve a compatibility problem between bisimulation relations arising from mobility and continuous behaviours.