Easy impossibility proofs for distributed consensus problems

Fischer, Michael J.; Lynch, Nancy; Merritt, Michael

doi:10.1145/323596.323602

Cited by 101 publications

(104 citation statements)

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“…Fischer, Lynch and Merritt [140] gave a similar proof to show that consensus is solvable in the presence of f arbitrary faults only if the connectivity is greater than 2f . Dolev [113] gave an f -resilient algorithm for terminating reliable broadcast provided the network has connectivity more than 2f and more than 3f processes.…”

Section: Bounds On the Number Of Faults In Synchronous Message-passinmentioning

confidence: 98%

“…Many variants of the consensus and set consensus problems, with slightly different agreement and validity properties, have been studied [109,138,140,163,218,234,254]. One example is the commit problem.…”

Section: Other Agreement Problemsmentioning

confidence: 99%

“…The following version of the argument, by Fischer, Lynch and Merritt [140], shows that consensus is impossible for three processes, P, Q and R, if one arbitrary process fault may occur. Suppose there is a consensus algorithm for this system.…”

Section: Bounds On the Number Of Faults In Synchronous Message-passinmentioning

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: Bounds On the Number Of Faults In Synchronous Message-passinmentioning

confidence: 98%

Section: Other Agreement Problemsmentioning

confidence: 99%

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Hundreds of impossibility results for distributed computing

Fich

Ruppert

2003

Distributed Computing

124

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“…It should be easy to see that if the multidimensional consensus is solved correctly with n ≤ 3 f , then scalar consensus is solved correctly. However, this contradicts [13]. Hence, n > 3 f is a necessary condition for multidimensional consensus with arbitrary d. Now we prove that n > (d + 1) f is also a necessary condition.…”

Section: Theoremmentioning

confidence: 73%

Multidimensional agreement in Byzantine systems

et al. 2015

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Consider a network of n processes, where each process inputs a d-dimensional vector of reals. All processes can communicate directly with others via reliable FIFO channels. We discuss two problems. The multidimensional Byzantine consensus problem, for synchronous systems, requires processes to decide on a single d-dimensional vector v ∈ R d , inside the convex hull of d-dimensional vectors that were input by the non-faulty processes. Also, the multidimensional Byzantine approximate agreement (MBAA) problem, for asynchronous systems, requires processes to decide on multiple d-dimensional vectors in R d , all within a fixed Euclidean distance of each other, and inside the convex hull of d-dimensional vectors that were input by the non-faulty processes. We obtain the following results for the problems (M. Herlihy) Supported by NSF 0830491. (N. Vaidya and V. K. Garg) above, while tolerating up to f Byzantine failures in systems with complete communication graphs: (1) In synchronous systems, n > max{3 f, (d + 1) f } is necessary and sufficient to solve the multidimensional consensus problem. (2) In asynchronous systems, n > (d + 2) f is necessary and sufficient to solve the multidimensional approximate agreement problem. Our sufficiency proofs are constructive, giving explicit protocols for the problems. In particular, for the MBAA problem, we give two protocols with strictly different properties and applications.

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“…In the literature, three different, but related, problems were addressed: consensus [6,9,11,12,13,19], agreement or interactive consistency [7,10,24], and leader election [2,3,5,8,15,16,17,20,25]. In the consensus problem, all of the non-faulty processors in the network want to agree on a single bit, a 0 or a 1.…”

Section: Literature Surveymentioning

confidence: 99%

Optimal asynchronous agreement and leader election algorithm for complete networks with Byzantine faulty links

Sayeed

Abu-Amara²,

Abu-Amara

1995

Distrib Comput

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We consider agreement and leader election on asynchronous complete networks when the processors are reliable, but some of the channels are subject to failure. Fischer, Lynch, and Paterson have already shown that no deterministic algorithm can solve the agreement problem on asynchronous networks if any processor fails during the execution of the algorithm. Therefore, we consider only channel failures. The type of channel failure we consider in this paper is Byzantine failure, that is, channels fail by altering messages, sending false information, forging messages, losing messages at will, and so on. There are no restrictions on the behavior of a faulty channel. Therefore, a faulty channel may act as an adversary who forges messages on purpose to prevent the successful completion of the algorithm. Because we assume an asynchronous network, the channel delays are arbitrary. Thus, the faulty channels may not be detectable unless, for example, the faulty channels cause garbage to be sent. We present the first known agreement and leader election algorithm for asynchronous complete networks in which the processors are reliable but some channels may be Byzantine faulty. The algorithm can tolerate up to [~-~] faulty channels, where n is the number of processors in the network. We show that the bound on the number of faulty channels is optimal. When the processors terminate their corresponding algorithms, all the processors in the network will have the same correct vector, where the vector contains the private values of all the processors.

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Easy impossibility proofs for distributed consensus problems

Cited by 101 publications

References 10 publications

Hundreds of impossibility results for distributed computing

Hundreds of impossibility results for distributed computing

Multidimensional agreement in Byzantine systems

Optimal asynchronous agreement and leader election algorithm for complete networks with Byzantine faulty links

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