Implementation of Symmetric Functions in Homogeneous Media

Two variants of a homogeneous medium are discussed. In the first variant the complexity of the implementation of an arbitrary symmetric function has order $C_1n^2$, where $C_1=1/2$; in the second variant it has order $n\log_2n(1+0(1))$. Thus, a bound is obtained on the complexity that can be realized by modeling of the schema of a symmetric function in a homogeneous medium by the method of Barzdin' [Probl. Kibern., vol. 17, Nauka, Moscow, 1966, pp. 5–26].