Polynomially Complete Fault Detection Problems

We look at several variations of the single fault detection problem for combinational logic circuits and show that deciding whether single faults are detectable by input-output (I/O) experiments is polynomially complete, i.e., there is a polynomial time algorithm to decide if these single faults are detectable if and only if there is a polynomial time algorithm for problems such as the traveling salesman problem, knapsack problem, etc.