Counting interfaces for discrete time modeling

A class of interfaces is introduced that are designed to model time relations between events of a system in terms of occurrences of a reference event. The reference event generates a discrete time scale in that each occurrence produces a next graduation on the scale. It is shown how various kinds of causal connection between the "timed system" and one or several reference events or "timers" can be achieved by counting the occurrences of the reference event(s). Since reference events belong to the considered system, their scopes as timers for other events can be chosen as needed and are visible in the model. Requirements referring to a local time or several independent times in the same system can thus be specified without making assumptions which are foreign to the model and are of possibly opaque consequences for implementation. Elementary and high-level Petri nets are used for modeling counting interfaces.