Mutually disjoint signals and probability calculation in digital circuits

Abstract

Signal probability calculation in circuits where signals are not independent is generally expensive. We show that some correlated signals may be mutually disjoint. In such cases, the probability calculation can be as simple as it is for independent signals. For example, two signals that cannot be simultaneously true are defined as OR-disjoint. If these signals feed an OR gate, the probability of the output being true is simply the sum of the probabilities of inputs being true. We give an implication-based algorithm for identifying disjoint signals. Examples of large adders illustrate how the identification of disjoint signals simplifies the probability calculation.