Polynomial ideal theory methods in discrete event, and hybrid dynamical systems

An attempt is made to rephrase selected properties relevant to discrete-event or hybrid dynamical systems in terms of nonlinear systems over finite fields. The advantages of this approach is twofold: first, it reveals that all operations are based on a single building block (computing the Grobner basis of suitable ideals), and second, the framework obtained is quite familiar to the control community. All this work generalizes immediately to finite fields F_p for any prime integer p