On the causality of mixed-signal and hybrid models

This paper extends the application of the Cantor metric as a mathematical tool for defining causalities from pure discrete models to mixed-signal and hybrid models. Using the Cantor metric, which maps timed signals, continuous or discrete, into a metric space, we define causality as contractive properties of processes operating on these signals. Thus, the Banach fixed point theorem can be-applies to establish conditions for the existence, uniqueness, and liveness of the behaviors for mixed-signal and hybrid systems. The results also provide theoretical foundations for the simulation technologies for such systems, including the time-marching strategy, evaluation of feedback loops, and the necessity of supporting rollback.