Abstract
Real-time and embedded applications often involve different types of timing constraints, such as precedence constraints and real-time constraints. As real-time and embedded applications further advance, new timing constraint types are emerging as well. Recent research on interval-based timing constraints is an example. Thus, it is important to have a uniformed timing constraint representation so that a generalized approach can be developed to analyze the variant constraint types.
A semiring-based timing constraint model is introduced to generalize the representations of different constraint types. Under this model, we develop an algorithm to check the satisfaction feasibility for a given set of semiring-based timing constraints. This algorithm provides better performance in the average case as compared to applying the Bellman-Ford algorithm directly on the constraint set.
In addition, for a set of feasible semiring-based timing constraints, event occurrence points that satisfy the constraint set form a (hyperdimension) feasible region. For the given two sets of timing constraints, we develop a necessary and sufficient condition to testify whether the two constraint sets' feasible regions have an inclusion relation. If one feasible region is included in the other, we know that the real-time event occurrences that satisfy the included constraint set will necessarily satisfy the including set.
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Index Terms
Feasibility of semiring-based timing constraints
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