Renaming in an Asynchronous Environment

This paper is concerned with the solvability of the problem of processor renaming in unreliable, completely asynchronous distributed systems. Fischer et al. prove in [8] that “nontrivial consensus” cannot be attained in such systems, even when only a single, benign processor failure is possible. In contrast, this paper shows that problems of processor renaming can be solved even in the presence of up to t < n/2 faulty processors, contradicting the widely held belief that no nontrivial problem can be solved in such a system. The problems deal with renaming processors so as to reduce the size of the initial name space. When only uniqueness of the new names is required, we present a lower bound of n + 1 on the size of the new name space, and a renaming algorithm that establishes an upper bound on n + t. If the new names are required also to preserve the original order, a tight bound of 2′1990 - 1 is obtained.