Short fault detection tests of contact break for contact circuits with an additional pole

We consider a problem of synthesis of three-pole contact circuits with poles $A$, $B$ and $V$ implementing given Boolean functions between poles $A$ and $B$ and allowing short fault detection tests regarding contact breaks. For each Boolean function of $n$ variables and each test pole set containing at least one of the pairs $\{A,V\},\{B,V\}$, the minimal possible length values of single and complete fault detection tests are found. In particular, it is proved that these values do not exceed $3$.