Discrete-event systems are a generalization of discrete-time systems that allow time to be continuous. The trajectories of a discrete-event system are functions from the time base to its sets of input, output, and state. These trajectories change value only a finite number of times in any finite interval. This is the defining characteristic of a discrete-event system; the events that cause these discrete changes give the class of systems its name.
The expanded time base raises two issues that are responsible for the relatively complicated (with respect to discrete-time systems) description of discrete-event systems and their simulators. The first is that events may occur at any instant. Consequently, the model must include machinery to describe the subset of where its events occur. The second is that time advances in a plane. Only the real part of this plane reflects physical time; the discrete part is an artifact of modeling change with instantaneous events (Maler and Manna offer an insightful discussion [82, 83]). The structure imposed on time to permit an orderly evolution of the system, although not complicated, is unlike the additive group typical of discrete time (i.e., with time base and differential (i.e., with time base systems.