Time Separation of Events: An Inverse Method

The problem of “time separation” can be stated as follows: Given a system made of several connected components, each one entailing a local delay known with uncertainty, what is the maximum time for traversing the global system? This problem is useful, e.g. in the domain of digital circuits, for determining the global traversal time of a signal from the knowledge of bounds on the component propagation delays. The uncertainty on each component delay is given under the form of an interval. The general problem is NP-complete. We focus here on the inverse problem: we seek intervals for component delays for which the global traversal time is guaranteed to be no greater than a specified maximum. We give a polynomial time method to solve it. As a typical application, we show how to use the method in order to relax some specified local delays while preserving the maximum traversal time. This is especially useful, in the area of digital circuits, for optimizing “setup” timings of input signals (minimum timings required for stability).