Strong Equivalence Relations for Iterated Models
The Iterated Immediate Snapshot model (IIS), due to its elegant geometrical representation, has become standard for applying topological reasoning to distributed computing. Its modular structure makes it easier to analyze than the more realistic (non-iterated) read-write Atomic-Snapshot memory model (AS). It is known that AS and IIS are equivalent with respect to wait-free task computability: a distributed task is solvable in AS if and only if it is solvable in IIS. We observe, however, that this equivalence is not sufficient in order to explore solvability of tasks in sub-AS models (i.e. proper subsets of AS runs) or computability of long-lived objects, and a stronger equivalence relation is needed.
In this paper, we consider adversarial sub-AS and sub-IIS models specified by the sets of processes that can be correct in a model run. We show that AS and IIS are equivalent in a strong way: a (possibly long-lived) object is implementable in AS under a given adversary if and only if it is implementable in IIS under the same adversary. Therefore, the computability of any object in shared memory under an adversarial AS scheduler can be equivalently investigated in IIS.
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