A combinatorial characterization of the distributed 1-solvable tasks

Biran, Ofer; Moran, Shlomo; Zaks, Shmuel

doi:10.1016/0196-6774(90)90020-f

Cited by 84 publications

(71 citation statements)

References 8 publications

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“…The reason is that a solution to any of these problems on G can be used to solve wait-free binary consensus, which is known to be impossible [5,20]. The following style of proof is known since the first (1-resilient) task characterization results [7].…”

Section: Impossibility Resultsmentioning

confidence: 99%

Convergence and covering on graphs for wait-free robots

2018

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The class of robot convergence tasks has been shown to capture fundamental aspects of fault-tolerant computability. A set of asynchronous robots that may fail by crashing, start from unknown places in some given space, and have to move towards positions close to each other. In this article, we study the case where the space is uni-dimensional, modeled as a graph G. In graph convergence, robots have to end up on one or two vertices of the same edge. We consider also a variant of robot convergence on graphs, edge covering, where additionally, it is required that not all robots end up on the same vertex. Remarkably, these two similar problems have very different computability properties, related to orthogonal fundamental issues of distributed computations: agreement and symmetry breaking. We characterize the graphs on which each of these problems is solvable, and give optimal time algorithms for the solvable cases. Although the results can be derived from known general topology theorems, the presentation serves as a self-contained introduction to the algebraic topology approach to distributed computing, and yields concrete algorithms and impossibility results.

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Section: Impossibility Resultsmentioning

confidence: 99%

Convergence and covering on graphs for wait-free robots

2018

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“…If there is a recent one (it is associated with a round greater than the round r start i at which p i has started simulating its current operation), p i keeps it in smin i (lines [8][9], and computes in last snap i the corresponding snapshot value of the shared memory (line 10). Finally, if p i observes that its last operation announced (that is identified est i [i]) appears in this vector, it returns last snap i (line 11).…”

Section: From Iris (Pr 3sx ) To the Read/write Model Equipped With 3s Xmentioning

confidence: 99%

“…end for; (6) esti ← maxCW{estj such that < j, estj, − >∈ smi}; (7) if ∃ρ > r starti such that ∃ < −, smin > such that ∀j ∈ smin : < j, smin >∈ viewi[ρ]¡ % there is a smallest snapshot in viewi[r starti + 1..ri] that is known by pi % (8) then let ρ be the greatest round ≤ ri that satisfies the previous predicate; (9) smini ← the smallest snapshot in viewi[ρ ]; (10) last snapi ← maxCW{estj such that < j, estj >∈ smini};…”

Section: From Iris (Pr 3sx ) To the Read/write Model Equipped With 3s Xmentioning

confidence: 99%

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The Iterated Restricted Immediate Snapshot Model

Rajsbaum¹,

Raynal

Travers

Lecture Notes in Computer Science

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Abstract:In the Iterated Immediate Snapshot model (IIS ) the memory consists of a sequence of one-shot Immediate Snapshot (IS ) objects. Each IS object can be accessed with an operation that atomically writes a value and returns a snapshot of its contents. Each process can access each IS object at most once. Processes access the sequence of IS objects, one-by-one, asynchronously, in a wait-free manner; any number of processes can crash. It has been shown by Borowsky and Gafni and others that this model is very useful to study the usual read/write shared memory model. Its interest lies in the elegant recursive structure of its runs, hence of the ease to analyze it round by round. In a very interesting way, Borowsky and Gafni have shown that the IIS model and the read/write model are equivalent for the wait-free solvability of decision tasks.In this paper we extend the benefits of the IIS model to partially synchronous systems. Given a shared memory model enriched with a failure detector, what is an equivalent IIS model? The paper shows that an elegant way of capturing the power of a failure detector and other partially synchronous systems in the IIS model is by restricting appropriately its set of runs, giving rise to the Iterated Restricted Immediate Snapshot model (IRIS ).The benefit of the proposed approach is new results (including new proofs of existing results) when we consider the IRIS model instead of the equivalent read/write model enriched with a given failure detector directly. As a study case, the paper considers a system enriched with limited-scope accuracy failure detectors, where there is a cluster of processes such that eventually some correct process is eventually never suspected by any process in that cluster. The paper provides a new proof of the k-set agreement Herlihy and Penso's lower bound for shared memory system augmented with a limited-scope accuracy failure detector. The proof is based on an extension of the Borowsky-Gafni IIS simulation to encompass failure detectors, followed by a very simple topological argumentation.With the IRIS model we have succeeded in capturing the partial synchrony of a failure detector enriched system via a fully asynchronous, round by round system. We thus hope to have contributed to a better understanding of fault-tolerant distributed computing. Key-words:Algorithmic reduction, Asynchronous system, Distributed algorithm, Distributed Computability, Failure detectors, Fault-tolerance, Round-based computation, Shared memory, Topology. IntroductionA distributed model of computation consists of a set of n processes communicating through some medium (some form of message passing or shared memory), satisfying specific timing assumptions (process speeds and communication delays), and failure assumptions (their number and severity). A major obstacle in the development of a theory of distributed computing is the wide variety of models that can be defined -many of which represent real systems -with combinations of parameters in both the (a)synchrony and failure dimen...

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“…THE NOTION OF LEGALITY. Given a condition C and a value for f , consider the graph Gin(C, f ) (close to the graph defined in Biran et al [1990a] (C, f ). Also, a connected component of Gin(C, f ) has one input value in common to all its vertices if and only if the corresponding component of H (C, f ) has at least one input value in common, and this value appears f + 1 times in each one of its vertices.…”

Section: A Characterization Of the Conditions For Consensus Solvabilitymentioning

confidence: 99%

Conditions on input vectors for consensus solvability in asynchronous distributed systems

Mostéfaoui

Rajsbaum²,

Raynal

2001

Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing

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Abstract. This article introduces and explores the condition-based approach to solve the consensus problem in asynchronous systems. The approach studies conditions that identify sets of input vectors for which it is possible to solve consensus despite the occurrence of up to f process crashes. The first main result defines acceptable conditions and shows that these are exactly the conditions for which a consensus protocol exists. Two examples of realistic acceptable conditions are presented, and proved to be maximal, in the sense that they cannot be extended and remain acceptable. The second main result is a generic consensus shared-memory protocol for any acceptable condition. The protocol always guarantees agreement and validity, and terminates (at least) when the inputs satisfy the condition with which the protocol has been instantiated, or when there are no crashes. An efficient version of the protocol is then designed for the message passing model that works when f < n/2, and it is shown that no such protocol exists when f ≥ n/2. It is also shown how the protocol's safety can be traded for its liveness.

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A combinatorial characterization of the distributed 1-solvable tasks

Cited by 84 publications

References 8 publications

Convergence and covering on graphs for wait-free robots

Convergence and covering on graphs for wait-free robots

The Iterated Restricted Immediate Snapshot Model

Conditions on input vectors for consensus solvability in asynchronous distributed systems

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