On the reliability of schemes in the basis $\{\vee,\&,\bar{}\,\}$ with single-type constant faults at the inputs of elements

We consider the realizations of Boolean functions in the basis $\{\vee,\&,\bar{}\,\}$ by circuits of unreliable functional elements which can have one-type constant faults at the inputs. We assume that elements transfer to fault states with probability $\gamma$ independent of each other. The unreliability of the circuit is defined as the maximal over all inputs probability of an error at the output of the circuit.
In the paper, a method of constructing reliable circuits consisting of unreliable elements is suggested, upper and lower bounds for the unreliability are obtained, the realization of all functions, except the constant functions, with maximal possible reliability (tending to one) is described. The constants are realized with reliability equal to one.
This research was supported by the Russian Foundation for Basic Research, grant 01–01–00053.