Generalized Automata and Their Net Representations

We consider two generalizations of the duality between transition systems and Petri nets. In the first, transitions are replaced by paths, that is partial functions from a fixed set ? to states. This allows to model continuous and/or hybrid systems when ? represents durations. In the second generalization actions are considered to have a structure given by an algebra. This allows to model, for instance, sequential and parallel composition of ordinary actions. In each case the question of the existence of a Galois connection is considered in the framework of ordered sets and in the categorical setting.