Efficient methods for computing an exact probability distribution of the delay of a combinational circuit, given probability distributions for the gate and wire delays, are developed. The derived distribution can give the probability that a combinational circuit will achieve a certain performance, across the possible range. This information can then be used to predict the expected performance of the entire circuit. The techniques presented target fast analysis as well as reduced memory requirements. The notion of a correct approximation, based on convex inequality, which never overestimates the percentage of circuits that will achieve any given performance is defined. It is shown that given the assumption that all the topologically longest paths are responsible for the delay, the computation technique provides a correct probabilistic measure in the sense given above. Methods are given to identify and to ignore false paths in the probabilistic analysis, so as to obtain correct and less pessimistic answers to the performance prediction question. Some practical results are given for a number of benchmark combinational circuits.
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