Refined Estimates of the Decoder Complexity in the Model of Cellular Circuits with Functional and Switching Elements

Abstract

The model of cellular circuits was considered in a single basis of functional and switching elements, which is built in accordance with the standard basis B 0 consisting of Boolean functions x 1 & x 2 , x 1 ∨ x 2 , x 1 . In this model, both circuit implementing such a decoder, provided that n = 1 , 2 , . . . , is equal to n 2 n − 1 (1+ O (1 /n )). This is the first time when so-called asymptotic estimates of a high degree of accuracy, i.e., estimates with a relative error O (1 /n ), were obtained for it.