Discrete-Time Scheduling under Real-Time Constraints

We introduce a new method for scheduling under real-time constraints that is suitable for synchronous system implementations. The input specification is in the form of timing diagrams in which the occurrence times of signal transitions or actions are related by linear constraints, expressing the assumptions on the input actions (the environment) and the commitments on the output actions. Provided that the specification is causal, we give an algorithm for deriving ASAP and ALAP relative schedules for the output actions. We then present a new algorithm for determining whether a given clock period is correct. Based on a schedule and a valid clock period, we transform the specification into a discretetime relative schedule. Such a schedule serves as the basis for implementing a synchronous state-machine controller.