Single fault detection tests for logic networks in the basis “conjunction-negation”

We consider a problem of synthesis of irredundant logic networks in the basis $\{\&,\neg\}$ and similar bases which implement Boolean functions on $n$ variables and allow short single fault detection tests regarding stuck-at-1 or stuck-an-0 faults on outputs of gates. For each Boolean function permitting implementation by an irredundant circuit, the minimal possible length value of such a test is found. In particular, it is proved that this value does not exceed three.