Impersonal Failure Detection

What does it mean to solve a distributed task? In Paxos, Lamport proposed a definition of solvability in which every process is split into a proposer that submits commands to be executed, an acceptor that takes care of the command execution order, and a learner that receives the outcomes of executed commands. The resulting perspective of computation in which every proposed command can be executed, be its proposer correct or faulty, proved to be very useful when processes take steps on behalf of each other, i.e., in simulations. Most interesting tasks cannot be solved asynchronously, and failure detectors were proposed to circumvent these impossibilities. Alas, when it comes to solving a task using a failure detector, we cannot leverage simulation-based techniques. A process cannot perform steps of failure detector-based computation on behalf of another process, since it cannot access the remote failure-detector module. This paper proposes a new definition of solving a task with a failure detector in which computation processes that propose inputs and provide outputs are treated separately from synchronization processes that coordinate using a failure detector. In the resulting framework, any failure detector is shown to be equivalent to the availability of some k-set agreement. As a corollary, we obtain a complete classification of tasks, including ones that evaded comprehensible characterization so far, such as renaming.