Short single tests for logic networks under arbitrary stuck-at faults at outputs of gates

We consider a problem of synthesis of irredundant logic networks implementing Boolean functions on $n$ variables and allowing short single tests regarding arbitrary stuck-at faults at outputs of gates. It is proved that one can implement any non-constant Boolean function by a network in the basis “conjunction, negation, sum of three variables modulo two”, allowing a single fault detection test with a length not exceeding $2$, and by a network in the basis consisting of one certain Boolean function on six variables, allowing a single diagnostic test with a length not exceeding $3$.