Tests of contact closure for contact circuits

The paper is concerned with the problem of synthesis of two-pole contact circuits implementing $n$-place Boolean functions and admitting short fault detection and diagnostic tests with respect to closures of contacts. It is shown that almost all $n$-place Boolean functions are implemented by irredundant two-pole contact circuits admitting single fault detection, complete fault detection and single diagnostic tests of constant length. We also prove that: \linebreak 1) any Boolean function $f(x_1,\ldots,x_n)$ may be implemented by an irredundant two-pole contact circuit containing at most one input variable distinct from the variables $x_1,\ldots,x_n$ and admitting single and complete fault detection tests of length at most $2n$; \linebreak 2) any Boolean function $f(x_1,\ldots,x_n)$ may be implemented by an irredundant two-pole contact circuit containing at most two input variables distinct from the variables $x_1,\ldots,x_n$ and admitting single diagnostic test of length at most $4n$.