ON BASES IN WHICH ASYMPTOTICALLY OPTIMAL CONNECTIONS FUNCTION WITH UNRELIABILITY 5 ε

Vasin Aleksey Valeryevich, Assistant, sub-department of discrete mathematics, Penza State University, alvarvasin@mail.ru

 519.718

We consider realization of Boolean functions by circuits composed of unreliable functional elements in some complete finite basis B ∈B₃ (  B₃ is the set of all Boolean functions of three variables x₁, x₂, and x₃). We assume that all elements are subjected independently of each other to inverse failures at the output with the probability ε(ε∈(0, 1/2)). In this article we found bases, in which almost all boolean functions is possible to realize by asymptotically optimal on reliability circuits with unreliability equal 5ε with ε→0. We proved that there are not other bases where it’s possible to realize almost all boolean functions by asymptotically optimal on reliability circuits with unreliability 5ε.

ненадежные функциональные элементы, асимптотически оптимальные по надежности схемы, инверсные неисправности на выходах элементов, синтез схем из ненадежных элементов.