Possibility and impossibility results in a shared memory environment

Taubenfeld, Gadi; Moran, Shlomo

doi:10.1007/s002360050034

Cited by 26 publications

(6 citation statements)

References 21 publications

(34 reference statements)

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“…Taubenfeld and Moran [292] used a valency argument to provide a general impossibility result for a large class of problems in asynchronous systems with crash failures, where processes communicate using registers. In particular, they show that there is no f -resilient algorithm for the consensus problem restricted to input vectors in which the number of 0's and the number of 1's differ by at least f .…”

Section: Asynchronous Shared-memory Modelsmentioning

confidence: 99%

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Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

124

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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, fault-tolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing. There is a strong emphasis in our presentation on explaining the wide variety of techniques that are used to obtain the results described.

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Section: Asynchronous Shared-memory Modelsmentioning

confidence: 99%

“…For example, a sharedmemory system can simulate a message-passing system with the same number of processes by using a single-writer single-reader register that can be written to by P and read by P to represent a communication channel from P to P [47,292]. Then, as mentioned in Sect.…”

Section: Relationships Between Modelsmentioning

confidence: 99%

Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

124

View full text Add to dashboard Cite

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“…Taubenfeld and Moran [1996] showed that binary consensus is solvable using a condition equivalent to this one.…”

mentioning

confidence: 92%

“…Agreement problems with a restricted set of inputs vectors were considered in Taubenfeld et al [1994] and Taubenfeld and Moran [1996], where possibility and impossibility results in a shared memory system and a hierarchy of problems that can be solved with up to f failures but not for ( f + 1) failures are introduced. More generally, an approach for designing algorithms in situations where there is some information about the typical conditions that are encountered when the respective problem is solved is presented in Berman and Garay [1998].…”

Section: Introductionmentioning

confidence: 99%

Conditions on input vectors for consensus solvability in asynchronous distributed systems

Mostéfaoui

Rajsbaum²,

Raynal

2003

J. ACM

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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. Abstract Devices]: Models of Computation-relations A preliminary version of this article appeared in

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“…To our knowledge, the idea to consider restricted sets of input vectors for consensus was stated for the first time in [27,28], where possibility and impossibility results in a shared memory system are presented. Moreover, these papers define a strict hierarchy of problems that can be solved in the presence of up to f failures but not in the presence of (f + 1) failures; they illustrate the hierarchy with variants of the consensus problem.…”

Section: Introductionmentioning

confidence: 99%

Condition-based consensus solvability: a hierarchy of conditions and efficient protocols

Mostéfaoui

Rajsbaum²,

Raynal

et al. 2004

Distributed Computing

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The condition-based approach for consensus solvability consists of identifying sets of input vectors, called conditions, for which there exists an asynchronous protocol solving consensus despite the occurrence of up to f process crashes. This paper investigates C f , the largest set of conditions which allow us to solve the consensus problem in an asynchronous shared memory system.The first part of the paper shows that C f is made up of a hierarchy of classes of conditions, CWe prove that each one is strictly contained in the previous one: CVarious properties of the hierarchy are also derived. It is shown that a class can be characterized in two equivalent but complementary ways: one is convenient for designing protocols while the other is for analyzing the class properties. The paper also defines a linear family of conditions that can be used to derive many specific conditions. In particular, for each d, two natural conditions are presented.The second part of the paper is devoted to the design of efficient condition-based protocols. A generic conditionbased protocol is presented. This protocol can be instantiated with any condition C, C ∈ C [d] f , and requires at most (2n+1) log 2 ( (f − d)/2 + 1) shared memory read/write operations per process in the synchronization part of the protocol. Thus, the value (f − d) represents the "difficulty" of the class C [d] f . An improvement of the protocol for the conditions in C[0] f is also presented.

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Possibility and impossibility results in a shared memory environment

Cited by 26 publications

References 21 publications

Hundreds of impossibility results for distributed computing

Hundreds of impossibility results for distributed computing

Conditions on input vectors for consensus solvability in asynchronous distributed systems

Condition-based consensus solvability: a hierarchy of conditions and efficient protocols

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