Achievable cases in an asynchronous environment

The paper deals with achievability of fault tolerant goals in a completely asynchronous distributed system. Fischer, Lynch, and Paterson [FLP] proved that in such a system "nontrivial agreement" cannot be achieved even in the (possible) presence of a single "benign" fault. In contrast, we exhibit two pairs of goals that are achievable even in the presence of up to t ≪ n/2 faulty processors, contradicting the widely held assumption that no nontrivial goals are attainable in such a system. The first pair deals with renaming processors so as to reduce the size of the initial name space. When only uniqueness is required of the new names, we present a lower bound of n + 1 on the size of the new name space, and a renaming algorithm which establishes an upper bound of n + t. In case the new names are required also to preserve the original order, a tight bound of 2t(n- t + 1) - 1 is obtained. The second pair of goals deals with the multi-slot critical section problem. We present algorithms for controlled access to a critical section. As for the number of slots required, a tight bound of t + 1 is proved in case the slots are identical. In the case of distinct slots the upper bound is 2t + 1.