The decidability of distributed decision tasks (extended abstract)

A task is a distributed coordination problem in which each process starts with a private input value taken from a tlnite set, communicates with the other processes by applying operations to shared objects, and eventually halts with a private output value, also taken from a finite set. A protocol is a distributed program that solves a task. A protocol is t-resikent if it tolerates failures by t or fewer processes. A task is solvable in a given model of computation if it has a t-resilientprotocol in that model. A set of tasks is decidable in a given model of computation if there exists an effective procedure for deciding whether any task in that set has a t-resilient protocol. This paper gives the first necessary and sufficient conditions for task decidability in a range of different models and resilience levels. We prove undecidability by exploiting classical decidabilit y results from algebraic topology, and we prove decidability by explicit construction.

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