When modelling complex systems, complexity is usually not only due to a large number of coupled components (submodels) , but also to the (perceived) diversity of these components and to their intricate interactions (i.e., high degree of feedback). One would like to use a variety of formalisms (DAE, Bond Graph, Forrester System Dynamics, Petri Nets, Finite State Automata, DEVS, State Charts, Queueing networks, . . . ) to "optimally" describe the behaviour of different system components, aspects, and views. The choice of appropriate formalisms depends on criteria such as the application domain, the modeler's background, the goals, and the available computational resources. In this article, a Formalism Tranformation Graph (FTG) is presented. In the FTG, vertices correspond to formalisms, and edges denote existing formalism transformations. A transformation is a mapping of models in the source formalism onto models in the destination formalism (with behaviour invariance). This traversal a...

Abstract. This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.