t-Resilient k-Immediate Snapshot and its Relation with Agreement Problems
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An immediate snapshot object is a high level communication object, built on top of a read/write distributed system in which all except one processes may crash. It allows a process to write a value and obtain a set of values that represent a snapshot of the values written to the object, occurring immediately after the write step. Considering an n-process model in which up to t processes may crash, this paper introduces first the k-resilient immediate snapshot object, which is a natural generalization of the basic immediate snapshot (which corresponds to the case k=t=n-1). In addition to the set containment properties of the basic immediate snapshot, a k-resilient immediate snapshot object requires that each set returned to a process contains at least (n-k) pairs. The paper first shows that, for k,t<n-1, k-resilient immediate snapshot is impossible in asynchronous read/write systems. the space of objects that read/write systems. Then the paper investigates a model of computation where the processes communicate with each other by accessing k-immediate snapshot objects, and shows that this model is stronger than the t-crash model. Considering the space of x-set agreement problems (which are impossible to solve in systems such that x≤ t), the paper shows then that x-set agreement can be solved in read/write systems enriched with k-immediate snapshot objects for x=max(1,t+k-(n-2)). It also shows that, in these systems, k-resilient immediate snapshot and consensus are equivalent when 1≤ t<n/2 and t≤ k≤ (n-1)-t. Hence, provides, the paper establishes strong relations linking fundamental distributed computing objects (one related to communication, the other to agreement), which are impossible to solve in pure read/write systems.
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