On the Respective Power of *P and *S to Solve One-Shot Agreement Problems

Unreliable failure detectors are abstract devices that, when added to asynchronous distributed systems, allow to solve distributed computing problems (e.g. Consensus) that otherwise would be impossible to solve in these systems. This paper focuses on two classes of failure detectors defined by Chandra and Toueg, namely, the classes denoted 3P (eventually perfect) and 3S (eventually strong). Both classes include failure detectors that eventually detect permanently all process crashes, but while the failure detectors of 3P eventually make no erroneous suspicions, the failure detectors of 3S are only required to eventually not suspect a single correct process. In such a context, this paper addresses the following question related to the comparative power of these classes, namely: “Are there one-shot agreement problems that can be solved in asynchronous distributed systems with reliable links but prone to process crash failures augmented with 3P, but cannot be solved when those systems are augmented with 3S?” Surprisingly, the paper shows that the answer to this question is “no”. An important consequence of this result is that 3P cannot be the weakest class of failure detectors that allows to solve one-shot agreement problems in unreliable asynchronous distributed systems. These results are then extended to the case of more severe failure modes. Key-words: Agreement Problem, Asynchronous Distributed System, Consensus, Computational Power, Input Vector, One-Shot Problem, Process Crash, Unreliable Failure Detector, 3P, 3S.