Hybrid dynamical systems theory and the Signal language

The logic and synchronization characteristics of general dynamical systems called hybrid dynamical systems (HDS) are studied. The theory is related to discrete event dynamical system theory, but handles numerics as well as symbolics. It is supported by the programming language Signal and a mathematical model of general implicit dynamical systems. The core of the theory is the notion of HDS resolution which is based on a coding of any HDS into a dynamic graph which consists of a skew product of a polynomial dynamical system on the finite field of integers modulo 3 (to describe the transitions of the underlying automation) and directed graphs (to describe how data dependencies dynamically evolve). The resolution algorithms are based on the study of this dynamical system