D. Dolev, R. Reischuk, and H. Strong. Early stopping in byzantine agreement. Journal of the ACM, 37(4):720--741, October 1990.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....expressing an upper bound on system reliability as the probability that t failures or less occur throughout the time the algorithm runs. Forgetting the relation between the t out of n assumption and system reliability can lead to a foolish design. For example, some consensus protocols (e.g. [7]) have a structure in which once t failures have been detected the protocol proceeds with the assumption that no further failures will occur. A more sensible design would have the protocol become more cautious under these circumstances: if t failures have occurred then it is possible that the ....

D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in Byzantine agreement. J. ACM, 37(4):720{ 741, October 1990.

....of the processes, receives messages, and does local processing. If a process fails in a given round, then any subset of the messages it sends in this round can be lost, and the process does not participate in any later rounds. In this paper we present a new lower bound proof for early deciding [3] uniform consensus. We show that in executions with f failures, uniform consensus requires f 2 rounds, for 0 f t 2. This is in contrast to non uniform consensus, which can be solved in f 1 rounds [12] Our proof is based on a very simple forward induction argument. A standard technique ....

D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. J. ACM, 37(4):720-741, October 1990.

....system with no communication. A generalization of this approach has recently been described by Koutsoupias and Papadimitriou [43] In addition, there is a long history of interest in optimality of a distributed algorithm given certain conditions, such as a particular pattern of failures [27, 31, 37, 50, 52, 53], or a particular pattern of message delivery [12, 33, 55] These and related works are in the spirit of our paper, but di er substantially in the details and applicability to distinct situations. In a sense, work on optimality envisions a fundamentally di erent role for the adversary in which it ....

D. Dolev, R. Reischuk, and H.R. Strong. Early Stopping in Byzantine Agreement. JACM 34:7, Oct. 1990.

.... every synchronous Consensus algorithm #, there is some execution in which some correct process does not decide earlier than # ##rounds, where # # # # ## # [1, 3, 12] Furthermore, there is some execution in which some correct process does not stop earlier than ##### #######rounds, for # # # # # [4]. These lower bounds were originally proved for crash failures, but they have to hold for arbitrary failures as well because the model of arbitrary failures is strictly weaker than the model of crash failures. In our model of dependent failures, however, the required number of rounds in general ....

....least five rounds to solve Consensus in the worst case. By executing SyncCrash with a minimum sized core as #, only three rounds are necessary in the worst case. In addition, no messages are broadcast by the processes in # # #. This differs in most algorithms designed under the # of # assumption [3, 4, 12], although the same idea can be applied by having only a specific subset of # ##processes broadcasting messages. In this latter case, however, the subset is not necessarily minimal. 6 Consensus for Arbitrary Failures Given a system configuration #### ### # #, consider the following properties: ....

D. Dolev, R. Reischuk, and H. R. Strong. Early Stopping in Byzantine Agreement. Journal of the ACM, 37(4):720--741, October 1990.

....We give an early deciding algorithm to solve CUP in a fail stop model, that is, in an asynchronous crash failure model with perfect failure detectors. The failure detector is external to CUP; it is implemented by Atom. CUP uses a strategy similar to previous early deciding consensus algorithms [10], but it also tolerates uncertainty about the set of participants, and moreover, it allows processes to leave voluntarily without incurring additional delays. The time required to reach consensus is linear in the number of failures that actually occur during an execution, and does not depend on ....

D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. Journal of the ACM, 37(4):720--741, Oct 1990.

....assumption 3, a lieutenant can determine if a traitorous lieutenant j k sends neither of these of those two messages. Alternatively, time out can be used to determine when no more messages will arrive. We may also refer to this situation as early stopping. This concept was used in Dolev s paper [17], when he explored the concept of early halting of the signed message algorithm. In step (2) lieutenant i ignores any messages that do not have the proper form of a value followed by a string of signatures. If packets of identical messages are used to avoid having to copy messages. A lieutenant ....

Dolev, D., Reischuk, R., and Strong, H.R., Early Stopping in Byzantine Agreement (1990) Journal of the ACM, vol.37 no. 4. pp720-741

....that is, in a timefree crash failure model where processes are equipped with perfect failure detectors [5] The failure detector is external to CUP; it is implemented by Atom. CUP uses a strategy similar to previous early deciding algorithms for consensus with a predetermined set of participants [13], but it also tolerates uncertainty about the set of participants, and moreover, it allows processes to leave voluntarily without incurring additional delays. The time required to reach consensus is linear in the number of failures that actually occur during an execution, and does not depend on an ....

D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. J. ACM, 37(4):720-741, October 1990.

....steps in failure free executions implicitly appears in their paper. Lamport [Lam00] shows a two communication steps bound for uniform consensus in the message omission model where processes do not crash, assuming the adversary is restricted so that consensus is solvable. Dolev et al. [DRS90] show that a consensus algorithm that can tolerate up to t n 1 crash failures will have executions with f failures involving a sequence of min(f 2; t 1) communication steps before all the processes halt. In contrast, we analyze here the time until all processes decide, which may be earlier ....

....model. The proof given in [MR98] for these two results actually works with the weaker weak validity property. However, the weaker weak validity property of [FLP85] does not suce for the f 2 lower bound for weak uniform consensus, nor for the f 2 lower bound on halting in consensus due to [DRS90], as we now show. In Figure 2, we give a counter example algorithm that satis es uniform agreement, termination, and weak validity as de ned in [FLP85] It decides and halts after one communication step in every failure free execution. The counter example algorithm uses a uniform consensus ....

D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. Journal of the ACM, 37(4):720-741, October 1990.

....that can crash and f be the number of actual crashes. When the distributed system is synchronous and f t n Gamma 1 the GDC problem can be solved in min(t 1; f 2) rounds of computation 2 (a round is a pattern of message exchange) which has been shown to be optimal for synchronous systems [3]. This paper presents a distributed protocol that, assuming f t n, solves the GDC problem in min(f 2; t 1; n) rounds of computation in asynchronous distributed systems prone to process crashes but equipped with a perfect failure detector. This protocol allows for early decision. This is ....

....few failures. Interestingly, when there is no crash, the processes decide and stop in two communication steps. The most important property of the proposed protocol lies in its time optimality. When t 1 n, it does not require more rounds than the lower bound required in the synchronous model [3]. An immediate consequence is that, when we consider the GDC problem and assume t 1 n, a synchronous system does not allow for more efficient solutions that an asynchronous system equipped with a perfect failure detector. A solution to the GDC problem can be designed in executing n parallel ....

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Dolev D., Reischuk R. and Strong R., Early Stopping in Byzantine Agreement. Journal of the ACM, 37(4):720-741, April 1990.

.... byzantine failure model, have been originally stated with non uniform conditions [PSL80, LSP82] Afterwards, the problem specifications that have been studied were often non uniform specifications, even in the setting of benign failures: for example, numerous results have been stated for consensus [FLP85, DDS87, DLS88, DRS90, DM90, CT96], and only a few are about uniform consensus [DS84, NT90, Lyn96] Interestingly, Guerraoui [Gue95] showed that in most partially synchronous systems where processes may commit only crash failures, any algorithm that solves consensus also solves uniform consensus. In such systems, there is thereby ....

....where processes decide one round earlier than in any uniform consensus algorithm in most cases (0 # f # t 2) By refining time complexity analysis in this way, we show that uniform consensus is harder than consensus for the crash failure model. It is important to note that contrary to [DRS90], we consider the time at which processes decide and not the time at which they halt. This is motivated by the following reasons. From a practical viewpoint, it is clearly useful to determine the time when decisions are available. On the other hand, since the t 1 worst case lower bound result ....

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Danny Dolev, Rudiger Reischuk, and H. Raymond Strong. Early stopping in Byzantine agreement. Journal of the ACM, 37(4):720--741, October 1990.

....f 2. 2 Remark 1 Our algorithm does not require an a priori upper bound on the number of faults. All nonfaulty processes decide no later than phase f 2, where f is the number of faults that actually occur in the execution. In consequence, the algorithm is an early stopping algorithm (cf. [14]) If an upper bound f is known a priori, the algorithm can be modified so that, if p i has not yet decided when it makes a next phase transition from phase f 1 to phase f 2, then p i can immediately decide on (f 2) mod 2. Since p i decides no later than the end of phase f 2, there is no ....

Dolev, D., Reischuk, R., and Strong, H. R. Early stopping in Byzantine agreement. J. ACM 37, 4 (October 1990), 720--741.

....[14,20] and Distributed Firing Squad [1,4,22] For example, in Byzantine Agreement, each processor starts with an input bit and chooses an output bit. All nonfaulty processors must choose the same output bit and this bit must be some processor s input bit. In Simultaneous Byzantine Agreement [5,6], all nonfaulty processors must choose their output bit in the same round. One property all of these problems have in common is that they define the correct behavior of the nonfaulty processors, but they do not restrict the behavior of faulty processors in any way. This is usually because ....

Danny Dolev, Rudiger Reischuk, and H. Raymond Strong. Early stopping in Byzantine agreement. Journal of the ACM, 37(4):720--741, October 1990.

....system with no communication. A generalization of this approach has recently been described by Koutsoupias and Papadimitriou [43] In addition, there is a long history of interest in optimality of a distributed algorithm given certain conditions, such as a particular pattern of failures [28, 32, 37, 44 46], or a particular pattern of message delivery [14, 34, 48] In a sense, work on optimality envisions a fundamentally di erent role for the adversary in which it is trying to produce bad performance for both the candidate and champion algorithms; in contrast, the adversary used in competitive ....

Danny Dolev, Ruediger Reischuk, and H. Raymond Strong. Early stopping in Byzantine agreement. Journal of the ACM, 37(4):720-741, October 1990.

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D. Dolev, R. Reischuk, and H. Strong. Early stopping in Byzantine agreement. J. ACM, 37(4):720--741, 1990.

No context found.

D. Dolev, R. Reischuk, and H. Strong. Early stopping in byzantine agreement. Journal of the ACM, 37(4):720--741, October 1990.

No context found.

D. Dolev, R. Reiscuk, and H. R. Strong. Early Stopping in Byzantine Agreement. Journal of ACM, 37(4):720--741, 1990.

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D. Dolev, R. Reischuk, and H. R. Strong, \Early Stopping in Byzantine Agreement," Journal of the ACM, vol. 37, pp. 720-741, October 1990.

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D. Dolev, R. Reischuk, and H. R. Strong, \Early Stopping in Byzantine Agreement," Journal of the ACM, vol. 37, pp. 720-741, October 1990.

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D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. J. ACM, 37(4):720-741, October 1990.

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D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. J. ACM, 37(4):720-741, October 1990.

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D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in byzantine agreement. J. ACM, 37(4):720--741, October 1990.

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Dolev D., Reischuk R. and Strong R., Early stopping in byzantine agreement. Journal of the ACM (JACM), 37(4):720-741, 1990.

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D. Dolev, R. Reischuk, and H. R. Strong. Early Stopping in Byzantine Agreement. Journal of the ACM, 37(4):720--741, October 1990.

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D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in Byzantine agreement. Technical Report RJ5406, IBM Research Laboratory, December 1986.

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D. Dolev, R. Reischuk, and H. R. Strong. Early stopping in Byzantine agreement. Journal of the ACM, 37(4), pages 720--741, 1990.

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