Delays of schemes in a model that considers the input values of functional elements

Abstract

A delay model for schemes of functional elements in arbitrary finite complete basis B is studied; in the model, delays of the basic element are given by random positive real numbers for each input and each input set of variables entering other inputs. Asymptotic estimates in the form τ B n ± O(logn), where τ B is a constant that depends only on basis B, are obtained for the delay of the multiplex function of order n. Based on these estimates, asymptotic estimates of the form τ B n ± O(logn) for the corresponding Shannon function, i.e., for the delay of the worst function of logic algebra that depends on given n variables, are established.