Time separations of cyclic event rule systems with min–max timing constraints

The analysis of the time separations of events is a fundamental problem in the design and evaluation of discrete event systems. Important progresses have been made based on the event rule system model in the last decade. The existing results for event rule systems with min and max constraints can be summarized briefly as: the exact evaluation of time separations for acyclic systems is NP-complete; for cyclic systems, the structural condition of being tightly coupled is sufficient for long-term time separations of events to be bounded. In this paper, we establish a necessary and sufficient structural boundedness condition—uniformity for cyclic event rule systems with both min and max constraints. Tightly coupled systems are shown to be a special class of uniform systems. The well-known CAS algorithm for finding bounds on long-term time separations is adapted to find finite bounds for uniform systems. Our results are obtained by exploring the algebraic structures guiding the evolution of the systems.