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... most “left behind” process in the currently simulated run. Even if the RAP-based simulation “blocks” because of a disagreement between the simulators (unavoidable in asynchronous fault-prone systems =-=[6]-=-), we guarantee that the most recent view of the blocked process is eventually noticed by more advanced simulated processes. • To obtain our “IIS to AS’ simulation, called FL (for fast-to-live), we ex...

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...ead-write Atomic-Snapshot model (AS) in which every process accesses persistent memory by alternating updates of its dedicated memory location with taking atomic snapshots of the whole memory content =-=[1]-=-. The conventional AS model can easily implement IIS using a distinct instance of the one-shot IS implementation [3] for every memory Mk. The opposite claim is in general not true, since the IIS model...

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...herefore, in terms of (wait-free) task computability, the two models have the same power. The equivalence turned out to be instrumental, e.g., in deriving the impossibility of wait-free set agreement =-=[2, 15]-=-. More generally, the equivalence enables the topological characterization of task solvability in AS [15, 12]. Unfortunately, the algorithms of [3, 4, 11] may be hard to use for establishing equivalen...

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...uple of minor proofs are delegated to the optional appendix. 2 Related work The IIS model introduced by Borowsky and Gafni [4] has become standard in topological reasoning about distributed computing =-=[14, 2, 4, 15, 12]-=-. The IIS model is precisely captured by the standard chromatic subdivision of the input complex [18, 16], and thus enables intuitive and elegant reasoning about its computability power, in particular...

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...n-closed memories M1, M2, . . .. The most popular one is the Iterated Immediate Snapshot model (IIS) [4]. Processes access the memories one by one, each time invoking the immediate snapshot operation =-=[3]-=- that writes to the memory and returns a “closely following” snapshot of the memory contents. Once memory Mk is accessed, a process never comes back to it. We contrast IIS with the more realistic read...

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...of live, resp. fast, processes. The relations between different simulation protocols are summarized in the following table: live(IIS) ⊆ fast(AS) fast(AS) ⊆ live(IIS) From IIS to AS Borowsky and Gafni =-=[4]-=- X ∃p ∈ fast(IIS) : p ∈ live(AS) Gafni and Rajsbaum [11] X ∃X ⊆ fast(IIS) : X ⊆ live(AS) This paper X X From AS to IIS Borowsky and Gafni [3] ∃p ∈ live(AS) : p ∈ fast(IIS) X This paper X X Together wi...

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...) [9]. This protocol guarantees agreement and validity. Moreover, if all proposed values are the same, then the algorithm terminates. This feature is implemented using the commit-adopt (CA) algorithm =-=[8]-=-. Otherwise, if two different values are proposed, the agreement algorithm may reach the blocked state. The blocked state can be resolved by the simulated process itself: the simulated process writes ...

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...d Gafni [4] has become standard in topological reasoning about distributed computing [14, 2, 4, 15, 12]. The IIS model is precisely captured by the standard chromatic subdivision of the input complex =-=[18, 16]-=-, and thus enables intuitive and elegant reasoning about its computability power, in particular, distinguishing solvable and unsolvable. At the same time, the IIS model is, in a precise sense, equival...

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...y and Rajsbaum [13] also considered the problem of two-way simulations between iterated and non-iterated models, but their results only concern t-resilient models and colorless tasks. Rajsbaum et al. =-=[20]-=- introduced the Iterated Restricted Immediate Snapshot (IRIS ) framework, where the restriction is defined via a specific failure detector on the per-round basis (not necessarily affecting the set of ...

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...ucceeds in simulating infinitely many 1 ar X iv :1 40 2. 24 46 v1s[ cs .D C]s1 1 F ebs20 14 reads and writes. This algorithm was later generalized to L-resilient adversaries [9] by Gafni and Rajsbaum =-=[11]-=-, where L is a superset-closed adversary [5, 17], defined as a superset-closed collection of correct sets. In [11], at least one correct set appears live in the simulated run. Therefore, AS and IIS (w...

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...rned out to be instrumental, e.g., in deriving the impossibility of wait-free set agreement [2, 15]. More generally, the equivalence enables the topological characterization of task solvability in AS =-=[15, 12]-=-. Unfortunately, the algorithms of [3, 4, 11] may be hard to use for establishing equivalences between sub-models of AS and IIS, i.e., proper subsets of their runs. Take, for example, the tresilient m...

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...lation presented in Section 5 is based on the non-blocking simulation of [4], with the helping mechanism similar to the one used in the original atomic snapshot construction [1]. Herlihy and Rajsbaum =-=[13]-=- also considered the problem of two-way simulations between iterated and non-iterated models, but their results only concern t-resilient models and colorless tasks. Rajsbaum et al. [20] introduced the...

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... set of live processes in an AS run coincides with the set of fast processes in the simulated IIS run, and vice versa. 1 Introduction Iterated memory models for distributed computing (see a survey in =-=[19]-=-) are like Fast Fourier Transform for communication: without them reasoning becomes hard and messy. In an iterated model, a set of processes pass through a series of disjoint communication-closed memo...

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...iv :1 40 2. 24 46 v1s[ cs .D C]s1 1 F ebs20 14 reads and writes. This algorithm was later generalized to L-resilient adversaries [9] by Gafni and Rajsbaum [11], where L is a superset-closed adversary =-=[5, 17]-=-, defined as a superset-closed collection of correct sets. In [11], at least one correct set appears live in the simulated run. Therefore, AS and IIS (we call the two models wait-free as they put no r...

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...IS) X This paper X X Together with a companion paper [10], this paper appears to be the first to formally define the notion of a fast process in IIS, streamlining the intuitive definition proposed in =-=[7]-=-. In [10], the equivalence between adversarial restrictions of AS and IIS is used to establish a generalized topological characterization of task computability. Our AS-to-IIS simulation presented in S...

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...tely many steps) process succeeds in simulating infinitely many 1 ar X iv :1 40 2. 24 46 v1s[ cs .D C]s1 1 F ebs20 14 reads and writes. This algorithm was later generalized to L-resilient adversaries =-=[9]-=- by Gafni and Rajsbaum [11], where L is a superset-closed adversary [5, 17], defined as a superset-closed collection of correct sets. In [11], at least one correct set appears live in the simulated ru...

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...d Gafni [4] has become standard in topological reasoning about distributed computing [14, 2, 4, 15, 12]. The IIS model is precisely captured by the standard chromatic subdivision of the input complex =-=[18, 16]-=-, and thus enables intuitive and elegant reasoning about its computability power, in particular, distinguishing solvable and unsolvable. At the same time, the IIS model is, in a precise sense, equival...