Peculiarities of the realization of boundedly deterministic functions by schemes of unreliable elements

We consider problems of the reliability of schemes of unreliable elements. This problem was first considered by von Neumann. He proved that in the case when the basis consists of functional elements and delays for an arbitrary boundedly deterministic function which can be obtained from boundedly deterministic functions of the basis using only the operation of superposition, one can construct a scheme of unreliable elements which realizes it with the probability of error approaching zero as the probability of error of the elements approaches zero.
We show that in the case of arbitrary boundedly deterministic functions this result does not hold.
We also consider a problem on the reliability of the realization of boundedly deterministic functions by means of schemes of unreliable elements in arbitrary automaton bases.