Failure Detectors in Homonymous Distributed Systems (with an Application to Consensus)

Abstract

This paper is on homonymous distributed systems where processes are prone to crash failures and have no initial knowledge of the system membership (``homonymous'' means that several processes may have the same identifier). New classes of failure detectors suited to these systems are first defined. Among them, the classes $\HO$ and $\HS$ are introduced that are the homonymous counterparts of the classes $\Omega$ and $\Sigma$, respectively. (Recall that the pair $\langle \Omega, \Sigma\rangle$ defines the weakest failure detector to solve consensus.) Then, the paper shows how $\HO$ and $\HS$ can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge of the membership. One algorithm solves consensus with $\langle \HO, \HS\rangle$, while the other uses only $\HO$, but needs a majority of correct processes. Observe that the systems with unique identifiers and anonymous systems are extreme cases of homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class $\HO$ can be implemented with partial synchrony, while the analogous class $\AO$ defined for anonymous systems can not be implemented (even in synchronous systems). Hence, the paper provides us with the first proof showing that consensus can be solved in anonymous systems with only partial synchrony (and a majority of correct processes).