We consider realizations of Boolean functions by circuits composed of unreliable functional elements in some complete finite basis B. We assume that all elements independently of each other with the probability epsilon(epsilon is an element of (0; 1/2)) are subjected to inverse failures at the output. We construct Boolean functions phi(x1, x2, x3) such that the presence of at least one of them in the considered basis B guarantees the realizability of all three Boolean functions by circuits whose reliability does not exceed 2 epsilon + 144 epsilon(2) with epsilon <= 1/960. In addition, if B subset of B-3 \ G (B-3 is the set of all Boolean functions of three variables x1, x2, x3, and G is the set of Boolean functions such that each one of them is congruent either to x(1)(sigma 1) x(2)(sigma 2) boolean OR x(1)(sigma 1) x(3)(sigma 3) boolean OR x(2)(sigma 2) x(3)(sigma 3), or to x(1)(sigma 1) x(2)(sigma 2) circle plus x(3)(sigma 3), or to x(1)(sigma 1) x(2)(sigma 2) boolean OR x(2)(sigma 2) x(3)(sigma 3) (sigma(1), sigma(2), sigma(3) is an element of {0, 1})), then the presence of at least one of functions phi(x1, x2, x3) guarantees the realizability of almost all Boolean functions by asymptotically optimal (with respect to the reliability) circuits, whose unreliability equals 2 epsilon as epsilon -> 0.
