Short fault detection tests for contact circuits under arbitrary weakly connected faults of contacts

We prove that for any natural $k$, any Boolean function can be implemented by a two-pole contact circuit that is $k$-irredundant and allows a $k$-fault detection test of length no more than $3$ relative to arbitrary connected faults of contacts in groups, where each group consists of one closing and one opening contact. We establish that if the Boolean function is not self-dual, then this bound can be lowered to $2$.