Network delay in a model with inputs of functional elements

Abstract

We consider a model of delays in networks of functional elements in an arbitrary finite complete basis B, where the delays of basis elements are arbitrary positive real numbers for each input and each input set of variables going to the remaining inputs. This model estimates the delays in a multiplexer function of nth order asymptotically as τBn ± O(logn), where τB is a constant depending only on the basis B. On the basis of these estimates and within this model, asymptotic estimates of the form τBn ± O(logn) are obtained for the corresponding Shannon function, i.e., for the delay of the “worst” Boolean algebra function of given n variables.