Estimates for lengths of check and diagnostic tests of functional elements

We examine problems of check of repair and state diagnosis of $N$ functional elements which realize a given Boolean function $f(x_1,\ldots,x_n)$ in their perfect states by means of composition of one-output circuits and observation of values produced by these circuits on any value sets of input variables. Random constant faults on outputs of functional elements are permitted; at the same time, it is assumed that not more than $k$ elements are faulted, where $k$ is a natural number that does not rank over $N$. It is needed to minimize a number of circuits required for check of repair and determination of states of all elements. It is shown that no more than $k$ circuits are required for each $f,N$, and $k$. For functions $f$ of special kind, necessary and sufficient conditions that $k$ circuits are enough for check of repair and state diagnosis of all elements are obtained. Ill. 3, bibliogr. 2.