Modeling Discretely Timed Systems Using Different Magnitudes of Non-standard Reals

Non-standard reals come in a number of magnitudes which is dense and which is bounded neither from the top nor from the bottom. This collection of magnitudes can be put to good use when a system is to be modeled at different time scales. As an application, we present quantitatively timed models of digital circuits, we discuss transient states of the system, and we show that under some plausible conditions, no tedious cycle-counting is necessary in order to establish freedom of hazards.