On reliability of circuits over an arbitrary complete finite basis under single-type constant faults at outputs of elements

We consider the realisation of Boolean functions by circuits with unreliable functional elements over an arbitrary complete finite basis B. It is assumed that all elements of the circuit are subject to single-type constant faults at the outputs which are independent of each other and occur with probability, gamma, gamma epsilon (0, 1/2). It is proved that all Boolean functions over the basis B can be realised by circuits with unreliability no greater than 3 gamma + 27 gamma(2) for all gamma epsilon (0,1/960). This research was supported by the Russian Foundation for Basic Research, grant 11-0100212a.