Asymptotic Bounds of the Shannon Function for a Depth Model of Functional-Element Networks with Capacity Parameters for Element Outputs

Abstract

The article proposes a synthesis method for amplifying networks of functional elements (ANFE) that establishes the asymptotic behavior of the Shannon function for the ANFE generalized depth, i.e., the depth of the “worst” Boolean function of n given variables, in a special basis (the depth model) where the element depth is determined both by its type and by its fan-out in the network. The asymptotic behavior of the Shannon function is established apart from a term logarithmic in n.