Fault diagnosis in a flash

Consider a set of n processors that can communicate with each other. Assume that each processor can be either “good” or “faulty”. Also assume that the processors can test each other. We consider how to use parallel testing rounds to identify the faulty processors, given an upper bound t on their number. We prove that 4 rounds are necessary and sufficient when 2√(2n)⩽0.03n (for n sufficiently large). Furthermore, at least 5 rounds are necessary when t⩾0.49n (for n sufficiently large), and 10 rounds are sufficient when t<0.5n (for all n). (It is well known that no general solution is possible when t⩾0.5n)