On diagnostic tests of contact break for contact circuits

We prove that, for $n\geqslant 2$, any $n$-place Boolean function may be implemented by a two-pole contact circuit which is irredundant and allows a diagnostic test with length not exceeding $n+k(n-2)$ under at most $k$ contact breaks. It is shown that with $k=k(n)\leqslant 2^{n-4}$, for almost all $n$-place Boolean functions, the least possible length of such a test is at most $2k+2$.