On Failure Detectors and Type Boosters

The power of a set S of object types can be measured as the maximum number n of processes that can solve consensus using only types in S and registers. This number, denoted by h^r_m (S), is called the consensus power of S. The use of failure detectors can however ``boost'' the consensus power of types. This paper addresses the weakest failure detector type booster question, which consists in determining the weakest failure detector D such that, for any set S of types with h_m^r(S)=n, h_m^r(S;D)=n+1. We consider the failure detector \Omega_n (introduced in (Neiger,1995)) which outputs, at each process, a set of at most n processes so that, eventually, all correct processes detect the same set of processes that includes at least one correct process. We prove that \Omega_n is the weakest failure detector type booster for deterministic one-shot types. As an interesting corollary of our result, we show that \Omega_f is the weakest failure detector to boost the power of (f-1)-resilient objects solving consensus.