Representing the behavior of multi-touch interactive systems in a complete, concise and non-ambiguous way is still a challenge for formal description techniques. Indeed, multi-touch interactive systems embed specific constraints that are either cumbersome or impossible to capture with classical formal description techniques. This is due to both the idiosyncratic nature of multi-touch technology (e.g. the fact that each finger represents an input device and that gestures are directly performed on the surface without an additional instrument) and the high dynamicity of interactions usually encountered in this kind of systems. This paper presents a formal description technique able to model multi-touch interactive systems. A layered architecture is also proposed that proposes a generic structure for organizing models of multi-touch systems. We focus the presentation on how to represent the dynamic instantiation of input devices (i.e. finger) and how they can then be exploited dynamically to offer a multiplicity of interaction techniques which are also dynamically instantiated.