The Disagreement Power of an Adversary

Delporte-Gallet, Carole; Fauconnier, Hugues; Guerraoui, Rachid; Tielmann, Andreas

doi:10.1007/978-3-642-04355-0_6

Cited by 28 publications

(44 citation statements)

References 13 publications

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“…The result has been generalized to the case of ¬Ω k and k-set consensus in [21]. Delporte et al [22] claimed to have concurrently derived the same result. Anta et al [23] showed that ¬Ω k is the weakest failure detector for solving k-set consensus in the special case of k-resilient environment E k .…”

Section: Related Workmentioning

confidence: 74%

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On set consensus numbers

Gafni

Kuznetsov

2011

Distrib. Comput.

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It is conjectured that the only way a failure detector (FD) can help solving n-process tasks is by providing k-set consensus for some k ∈ {1, . . . , n} among all the processes. It was recently shown by Zieliński that any FD that allows for solving a given n-process task that is unsolvable read-write wait-free, also solves (n − 1)-set consensus. In this paper, we provide a generalization of Zieliński's result. We show that any FD that solves a colorless task that cannot be solved read-write k-resiliently, also solves k-set consensus. More generally, we show that every colorless task T can be characterized by its set consensus number: the largest k ∈ {1, . . . , n} such that T is solvable (k − 1)-resiliently. A task T with set consensus number k is, in the failure detector sense, equivalent to k-set consensus, i.e., a FD solves T if and only if it solves k-set consensus. As a corollary, we determine the weakest FD for solving k-set consensus in every environment, i.e., for all assumptions on when and where failures might occur.

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Section: Related Workmentioning

confidence: 74%

“…Delporte et al [24] proposed a simulation of a protocol solving a colorless task using ¬Ω k that is similar in spirit to our construction in Sect. 5.…”

Section: Related Workmentioning

confidence: 97%

On set consensus numbers

Gafni

Kuznetsov

2011

Distrib. Comput.

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“…We can think of its generalization to any progress condition on computation processes encapsulated, e.g., in an adversary [19]. Therefore, we can pose questions of the kind: what is the weakest failure detector to solve a task T in the presence of an adversary A?…”

Section: Resultsmentioning

confidence: 99%

“…All tasks that can be solved k-concurrently but not (k + 1)-concurrently (e.g., k-set agreement) are equivalent in the sense that they require exactly the same amount of information about failures (captured by ¬ k ) to be solved in EFD. Note that this characterization covers all tasks, including "colored" ones that evaded any characterization so far [2,19,26].…”

Section: Ramificationsmentioning

confidence: 99%

“…One important feature inherited by our EFD framework from wait-free protocols is that it leverages simulation-based computing: processes can cooperate trying to bring all participating processes to their outputs. Simulations were instrumental in establishing tight relations between seemingly different phenomena in asynchronous systems [8,10,19,22,24,25,27], and we extend this line of research below to failuredetector models.…”

Section: Ramificationsmentioning

confidence: 99%

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Wait-freedom with advice

et al. 2014

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International audienceWe motivate and propose a new way of thinking about failure detectors which allows us to define what it means to solve a distributed task wait-free using a failure detector. In our model, the system is composed of computation processes that obtain inputs and are supposed to produce outputs and synchronization processes that are subject to failures and can query a failure detector. Under the condition that correct (never failing) synchronization processes take sufficiently many steps, they provide the computation processes with enough advice to solve the given task wait-free: every computation process outputs in a finite number of its own steps, regardless of the behavior of other computation processes. Every task can thus be characterized by the weakest failure detector that allows for solving it, and we show that every such failure detector captures a form of set agreement. We then obtain a complete classification of tasks, including ones that evaded comprehensible characterization so far, such as renaming or weak symmetry breaking

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Affine Tasks for k-Test-and-Set

Kuznetsov

Rieutord

2020

Lecture Notes in Computer Science

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The paper proposes a surprisingly simple characterization of task computability of the wait-free shared-memory model in which processes, in addition to read-write registers, have access to k-test-and-set objects. Our characterization is expressed in the form of an affine task : a subcomplex of some iteration of the standard chromatic subdivision. This appears to be the first topological characterization of a model in which processes communicate via long-lived objects beyond read-write registers.

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The Disagreement Power of an Adversary

Cited by 28 publications

References 13 publications

On set consensus numbers

On set consensus numbers

Wait-freedom with advice

Affine Tasks for k-Test-and-Set

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