The worst-case chip problem

In the system level, adaptive fault diagnosis problem we must determine which components (chips) in a system are defective, assuming the majority of them are good. Chips are tested as follows: Take two chips, say x and y, and have x report whether y is good or bad. If x is good, the answer is correct, but if x is bad, the answer is unreliable. One way to identify all defective chips is to identify a single good chip which can then be used to diagnose the other chips; the chip problem is to identify a single good chip. We show that the chip problem is closely related to a modified majority problem in the worst case and use this fact to obtain upper and lower bounds on algorithms for the chip problem.