Probabilistic Treatment of General Combinational Networks

In this correspondence two methods are given for calculating the probability that the output of a general combinational network is 1 given the probabilities for each input being 1. We define the notions of the probability of a signal and signal independence. Then several proofs are given to show the relationship between Boolean operations and algebraic operations upon probabilities. As a result of these, two simple algorithms are presented for calculating output probabilities. An example of the usefulness of these results is given with respect to the generation of tests for the purpose of fault detection.