Consensus in Anonymous Distributed Systems: Is There a Weakest Failure Detector?

This paper is on failure detectors to solve the consensus problem in asynchronous systems made up of anonymous processes prone to crash and connected by asynchronous reliable channels. Anonymity means that any two processes cannot be distinguished one from the other: they have no name and execute the same code. The paper has several contributions. It first introduces two new classes of failures detectors, denoted AP and AΩ, and presents an AP-based algorithm and an AΩ-based algorithm that solve the consensus problem despite the three computational adversaries that are asynchrony, failures and anonymity. Then, the paper shows that, in crash-prone non-anonymous systems, (a) AP and the class of perfect failure detectors (denoted P) are equivalent, and (b) AΩ and the class of eventual leader failure detectors (denoted Ω) are also equivalent. Finally, the paper addresses the question of the weakest failure detector to solve consensus in an asynchronous crash-prone anonymous system. In non-anonymous systems, the class P of perfect failure detectors is strictly stronger than the class Ω of eventual leader failure detectors that has been shown to be the weakest failure detector class for consensus in asynchronous crashprone system. Quite surprisingly, the paper shows that their anonymous counterparts cannot be compared. Hence, while Ω is the weakest failure detector class to solve consensus in non-anonymous systems, it is possible that there are several (hence incomparable) classes of weakest failure detectors for this problem in anonymous systems.