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Kuznetsov: Live Equals Fast in Iterated Models
 CoRR
, 2014
"... The Iterated Immediate Snapshot model (IIS), due to its elegant topological representation, has become standard for applying topological reasoning to distributed computing. In this paper, we focus on relations between IIS and the more realistic (noniterated) readwrite AtomicSnapshot memory model ..."
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The Iterated Immediate Snapshot model (IIS), due to its elegant topological representation, has become standard for applying topological reasoning to distributed computing. In this paper, we focus on relations between IIS and the more realistic (noniterated) readwrite AtomicSnapshot memory model (AS). We grasp equivalences between subsets of runs of AS and IIS (we call them subIIS and subAS models). To establish an equivalence between a subAS model M and a subIIS model M ′, we need two algorithms, a forward simulation F: AS → IIS and a backward simulation B: IIS → AS, such that B(F (M)) ⊆M and F (B(M ′)) ⊆M ′. AS and IIS are provided with such simulations and, thus, they have the same task computability power. However, the relations between proper subAS and subIIS models remained unclear until now. In this paper, we present a twoway simulation protocol that provides an equivalent subIIS model for any adversarial subAS model, i.e., for any subAS model specified by the sets of live processes. We achieve the result by ensuring that, under the twoway simulation, the set of live processes in an AS run coincides with the set of fast processes in the simulated IIS run, and vice versa. 1
A generalized asynchronous computability theorem
 CoRR
"... Abstract. We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be solvable in M. When applied to the waitfree model, our conditions result in the celebrated ..."
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Abstract. We consider the models of distributed computation defined as subsets of the runs of the iterated immediate snapshot model. Given a task T and a model M, we provide topological conditions for T to be solvable in M. When applied to the waitfree model, our conditions result in the celebrated Asynchronous Computability Theorem (ACT) of Herlihy and Shavit. To demonstrate the utility of our characterization, we consider a task that has been shown earlier to admit a very complex tresilient solution. In contrast, our generalized computability theorem confirms its tresilient solvability in a straightforward manner. 1.