Upper Bound on the Redundancy of Self-correcting Arrangements of Unreliable Functional Elements

The redundancy of self-correcting arrangements of functional elements that realize Boolean vector-valued functions is investigated. All functional elements of which the arrangements are composed are assumed to be unreliable; specifically, all elements make errors with probability $\varepsilon$ independently of one another and of the signals fed to them. The error probability for a particular output can be made close to $\varepsilon$. Upper bounds are obtained for the redundancy of such arrangements.