On the weakest failure detector ever

Abstract

Many problems in distributed computing are impossible when no information about process failures is available. It is common to ask what information about failures is necessary and sufficient to circumvent some specific impossibility, e.g., consensus, atomic commit, mutual exclusion, etc. This paper asks what information about failures is needed to circumvent any impossibility and sufficient to circumvent some impossibility. In other words, what is the minimal yet non-trivial failure information.We present an abstraction, denoted Υ, that provides very little failure information. In every run of the distributed system, Υ eventually informs the processes that some set of processes in the system cannot be the set of correct processes in that run. Although seemingly weak, for it might provide random information for an arbitrarily long period of time, and it only excludes one possibility of correct set among many, Υ still captures non-trivial failure information. We show that Υ is sufficient to circumvent the fundamental wait-free set-agreement impossibility. While doing so, we (a) disprove previous conjectures about the weakest failure detector to solve set-agreement and we (b) prove that solving set-agreement with registers is strictly weaker than solving n + 1-process consensus using n-process consensus.We prove that Υ is, in a precise sense, minimal to circumvent any wait-free impossibility. Roughly, we show that Υ is the weakest eventually stable failure detector to circumvent

The Weakest Failure Detector for Message Passing Set-Agreement

“…Several papers have been devoted to determine the weakest failure detector to solve the set-agreement problem in a distributed system where any number of processes can fail by crashing [7,8,9,10]. In particular, Zieliński proved recently that anti-Ω -a failure detector that outputs id's of processes such that the id of at least one correct process is output only finitely many times -is the weakest failure detector for set-agreement in a shared memory system [10].…”

“…In particular, Zieliński proved recently that anti-Ω -a failure detector that outputs id's of processes such that the id of at least one correct process is output only finitely many times -is the weakest failure detector for set-agreement in a shared memory system [10]. The proof of the result is particularly involved and builds on earlier proof techniques from [6] and [8].…”

“…We first give an algorithm that solves set-agreement using L. The particularity of the algorithm is its non-symmetric nature as it heavily exploits the total order on the identity of the processes. We then assume that there is an algorithm A that solves set-agreement (with some failure detector), and we show how to "extract" from A the output of L. Our approach here is, on the one hand, different from the approach of [6] where each process locally simulates several runs of A and, on the other hand, different from the approach of [10], as well as [8], where the extraction relies on the asynchronous impossibility of a problem. In our case, the processes execute one instance of A, without knowing the automaton of A performed at each process.…”

The Iterated Restricted Immediate Snapshot Model

“…According to the type and the quality of the hints, several classes of failure detectors have been defined (e.g., [13,18,29,32,37]). …”

The failure detector abstraction

“…For the case k = n − 1, the conjecture was later disproved by Guerraoui et al [2007] with a failure detector Υ. Υ outputs a non-empty set of processes, and eventually all correct processes stabilize on the same output set that is not the set of correct processes. Υ is strictly weaker than Ω n−1 but still strong enough to solve (n, n − 1)-set agreement.…”