**Authors:** Richard Beigel, William Hurwood, and Nabil Kahale

**Abstract:**
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 2sqrt(2*n*) ≤
*t* ≤ 0.03*n* (for *n* sufficiently large).
Furthermore, at least 5 rounds are necessary when *t* ≤
0.49*n* (for *n* sufficiently large), and 10 rounds are
sufficient when *t* < 0.5*n* (for all *n*). (It is
well known that no general solution is possible when *t* ≥
0.5*n*.)