On the impossibility of implementing perpetual failure detectors in partially synchronous systems

In this paper we study the implementability of different classes of failure detectors in several models of partial synchrony. We show that no failure detector with perpetual accuracy (namely, P, Q, S, and W) can be implemented in any of the models of partial synchrony proposed previously in systems with even a single failure. We also show that, in these models of partial synchrony, it is necessary for a majority of correct processes to implement a failure detector of class Θ