  As the size of a multiprocessor system increases, processor failure is
inevitable, and fault identification in such a system is crucial for reliable
computing. The fault diagnosis is the process of identifying faulty processors
in a multiprocessor system through testing. For the practical fault diagnosis
systems, the probability that all neighboring processors of a processor are
faulty simultaneously is very small, and the conditional diagnosability, which
is a new metric for evaluating fault tolerance of such systems, assumes that
every faulty set does not contain all neighbors of any processor in the
systems. This paper shows that the conditional diagnosability of bubble sort
graphs $B_n$ under the PMC model is $4n-11$ for $n \geq 4$, which is about four
times its ordinary diagnosability under the PMC model.
