H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122-152, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....a message, # # generating the response and the other parties receiving it is . If the network performance has a high variety, the timing uncertainty might be rather large. Therefore we de ne another timing constant for each run of the protocol. This timing model is similar to the one used in [ADLS94]. # The maximum time between # # receiving a message and other parties receiving the response during one execution of the protocol that occurs during one run of the protocol is #. 2 The value can be freely chosen and might be adapted to the network performance. Tighter bounds decrease the ....

H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122-152, January 1994.

....either there is a bound on message delay that is not known to the processes, or there is a known bound that applies only after some initial time T 0 . They describe consensus protocols for this model that work with a bound on the number of faulty processes. Attiya, Dwork, Lynch, and Stockmeyer [16] give a still more re ned model in which there are known bounds C on the ratio between the maximum and minimum real time between steps of the same process and d on the maximum message delay; under these assumptions, they prove an upper bound of (f 1)Cd and a lower bound of (f 1)d on the ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122-152, January 1994.

....higher layers of Isis can be built based on our approach. This is left as a subject for future research. 5.4 Other work Several works in fault tolerant computing used time outs primarily or exclusively for the purpose of failure detection. An example of this approach is given by an algorithm in [ADLS91] which, as pointed out by the authors, can be viewed as an asynchronous algorithm that uses a fault detection (e.g. timeout) mechanism. Appendix A A hierarchy of failure detectors and bounds on fault tolerance In the preceding chapters, we introduced the concept of unreliable failure ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainity. In Proceedings of the Twenty third ACM Symposium on Theory of Computing, May 1991.

....detector time out periods closer to the average case, while Isis must set time outs to the worst case. 9.4 Other work Several works in fault tolerant computing used time outs primarily or exclusively for the purpose of failure detection. An example of this approach is given by an algorithm in [ADLS91] which, as pointed out by the authors, can be viewed as an asynchronous algorithm that uses a fault detection (e.g. timeout) mechanism. Acknowledgements We are deeply grateful to Vassos Hadzilacos for his crucial help in revising this paper. The comments and suggestions of the anonymous ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainity. In Proceedings of the Twenty third ACM Symposium on Theory of Computing, pages 359--369. ACM Press, May 1991.

....other messages. This is implicit in the description below. Let k be a constant. Consider history H 3 (k) shown in Figure 18. In H 3 (k) processors in fbg[A 0 are faulty. All correct processors receive their first inputs at time 0 in H 3 . These inputs are identical to those they receive in H 1 [1]. Processors steps take 1=4k time units in H 3 (k) At time 0, all processors send their first message containing their first inputs to all other processor. Processor b sends 1 to processors in P Gamma C 0 and sends 0 to processors in C 0 . All first messages by processors in fbg [ A 0 [ A 1 ....

....a 1 2 A 1 , then (v q ; q) 1; b) 2 Now, we consider history H 4 shown in Figure 18. In H 4 , processors in fbg[A 1 are faulty (this is possible because jfbg [ A 1 j t) All correct processors receive their first inputs at time 0 in H 4 These inputs are identical to those they receive in H 1 [1]. All the steps of processors take 1 4 time unit in H 4 . At time 0, all processors send their first message containing their first input to all other processor. Processor b sends 1 to processors in A 1 [C 1 and 0 to all other processors. All first messages by processors fbg [A 0 [A 1 take 1 4 ....

[Article contains additional citation context not shown here]

H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. In Proceedings of the Twenty-Third ACM Symposium on Theory of Computing, pages 359--369. ACM Press, May 1991.

....models extended cleanly to the semi synchronous model. We consider this significant. Although variants of the semi synchronous model have been around for a long time, we are aware of only one substantial lower bound in this model: the consensus bound of Attiya, Dwork, Lynch, and Stockmeyer [ADLS94] The absence of other results suggests that it is very difficult to prove significant lower bounds in this model, and that results and proof techniques from other models do not translate into the semi synchronous model as easily as one might hope. With our pseudosphere construction, however, we ....

....in G receives exactly the same messages. The resulting protocol complex is not a pseudosphere, but it has the same homotopy type as an f dimensional pseudosphere (just contract each simplex spanned by processes in G to a point) Using this result and the execution stretching techniques from [ADLS94] we can prove that Corollary 32: Any wait free protocol for k set agreement and n 1 processes in the semi synchronous model requires time Xi n k Pi d Cd. As noted above, this corollary is the first substantial new lower bound for the semi synchronous model since the Attiya, Dwork, ....

[Article contains additional citation context not shown here]

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122--152, January 1994.

....periods closer to the average case, while systems like Isis must set time outs closer to the worst case. 9.4 Other work Several works in fault tolerant computing used time outs primarily or exclusively for the purpose of failure detection. An example of this approach is given by an algorithm in [Attiya et al. 1991], which, as pointed out by the authors, can be viewed as an asynchronous algorithm that uses a fault detection (e.g. timeout) mechanism. Recent work shows that the Group Membership problem cannot be solved in 25 For example, the time out period in the current version of Isis is greater than ....

Attiya, H., Dwork, C., Lynch, N., and Stockmeyer, L. 1991 . Bounds on the time to reach agreement in the presence of timing uncertainity. In Proceedings of the Twenty third ACM Symposium on Theory of Computing (May 1991), pp. 359--369. ACM Press.

....and or the communication can fail in a non stable period. In such a period: Some processes can crash, some messages can exceed their time bound and some steps of the processes can exceed the time bound c 2 . Let us suppose that the system is S stable. Using a timeout system like this one in [1], we can build failure detectors ensuring the sufficient properties to build a k synchronized SPS. More precisely, we can build exact trusted lists: Proposition 8 There exists a constant D, such that, for all executions, if the system is stable during [t 1 ; t 2 ] with t 2 Gamma t 1 D, then ....

H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. J. ACM, 41(1):122--152, Jan. 1994.

....two steps lead to di erent decision values. The other cases show that con gurations obtained by taking one or both of these steps are either identical or di er only in the state of one process, which can then be permanently halted by an adversarial scheduler. Attiya, Dwork, Lynch, and Stockmeyer [12] used valency arguments to give lower bounds on the time required to solve consensus in a semi synchronous message passing model, where messages are delivered within time d and there is a bound, r, on the ratio of process speeds. They proved that the worst case running time of a t resilient ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1), pages 122-152, 1994.

....models extended cleanly to the semi synchronous model. We consider this significant. Although variants of the semi synchronous model have been around for a long time, we are aware of only one substantial lower bound in this model: the consensus bound of Attiya, Dwork, Lynch, and Stockmeyer [ADLS94] The absence of other results suggests that it is very difficult to prove significant lower bounds in this model, and that results and proof techniques from other models do not translate into the semi synchronous model as easily as one might hope. With our pseudosphere construction, however, we ....

....in G receives exactly the same messages. The resulting protocol complex is not a pseudosphere, but it has the same homotopy type as an f dimensional pseudosphere (just contract each simplex spanned by processes in G to a point) Using this result and the execution stretching techniques from [ADLS94] we can prove that Corollary 30: Any wait free protocol for k set agreement and n 1 processes in the semi synchronous model requires time Xi n k Pi d Cd. As noted above, this corollary is the first substantial new lower bound for the semi synchronous model since the Attiya, Dwork, ....

[Article contains additional citation context not shown here]

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122--152, January 1994.

....of the work for shared memory systems mentioned above. In such systems, relative but unknown bounds are assumed on the speeds of network components, and efficient algorithms can be designed that exploit this synchrony assumption. Models slightly stronger than Archimedean systems are studied in [6, 5, 9, 15]. Two common notions used in the literature are those of non blocking and wait free objects [14] The first corresponds to implementations which are both fully resilient and deadlock free, while the second corresponds to implementations which are both fully resilient and starvation free. While ....

H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. In Proc. 23rd ACM Symp. on Theory of Computing, pages 359--369, May 1991.

....and we suppose a message is available for its process target in time at most ffi . We do not assume that the processes have access to synchronized clocks. Let us present the definitions for the underlying formal model. Essentially, it is a timed model. The presentation is rather similar to its of [ADLS94], but theses definitions could also be expressed in terms of timed automaton model [MMT91, Lyn96] A timed execution is an execution in which all events are timed. A timed event is a pair (e; t) where e is a computation event, and t, the time of event, is a nonnegative real number. A timed ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122--152, January 1994.

....and or the communication can fail in a non stable period. In such a period: Some processes can crash, some messages can exceed their time bound and some steps of the processes can exceed the time bound c 2 . Let us suppose that the system is S stable. Using a time out system like this one in [ADLS94] we can build failure detectors ensuring the sufficient properties to build a k synchronized SPS. More precisely, we can build exact trusted lists: Proposition 8. There exists D, such that, for all executions, if the system is stable during [t 1 ; t 2 ] with t 2 Gamma t 1 D, then during [t 1 ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122--152, January 1994.

....at most 4. Translations such as those presented in this paper have been developed for completely asynchronous systems [7] as well as the completely synchronous systems considered here. Other researchers have studied problems in which there exists timing uncertainty that is bounded. Attiya et al. [1] consider the consensus problem in such systems with crash failures. Ponzio [21] extends this work to systems with send omission and arbitrary failures. It seems likely that translations applicable to such systems would simplify the latter and may lead to improved algorithms. In fact, the ....

Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. In Proceedings of the Twenty-Third ACM Symposium on Theory of Computing, pages 359--369. ACM Press, May 1991.

....independent rate. Furthermore, the asynchrony assumption makes it very difficult to design and verify distributed algorithms whereas the perfect synchrony assumption is very expensive, if not impossible, to implement in distributed systems. Based on these observations, researchers (e.g. [ADLS91, AL89, AM90, CT90, CW90, DDS87, DLS88, Po91] ) began to investigate the impact on distributed computing if those timing assumptions are relaxed or tightened to some extent in order to reflect more realistic system situations. The new timing models that are obtained by relaxing or tightening the two extreme timing assumptions are called ....

....it is stronger than the asynchronous model enabling us to design algorithms for problems that are unsolvable in the asynchronous model. Models with known lower and upper bounds on step time are commonly called semi synchronous models and have been previously studied in the literature (see [AM90, AAT94, ADLS91, AL89, AT92, CT90, LS92, Po91, RW92]) and these results are reviewed in more detail in Section 1.6. The semi synchrony models systems 14 where information about process step time is only approximately known, e.g, processes may have access to inaccurate clocks that operate at approximately, but not exactly, the same rate. Models ....

[Article contains additional citation context not shown here]

H. Attiya, C. Dwork, N. Lynch and L. Stockmeyer, "Bounds on the Time to Reach Agreement in the Presence of Timing Uncertainty," Proc. 23rd ACM Symp. on Theory of Computing, 1991, pp. 359--369.

.... besides mutual exclusion that have been studied in the asynchronous setting (for example, other exclusion problems such as the dining philosophers problem, distributed consensus problem, or synchronization problems such as the session problem of [1 ] some results in this direction appear in [2, 3, 26, 27]. In addition to defining variants of asynchronous problems, one can also extract prototypical problems from practical real time systems research and use them as a basis for combinatorial work. In another direction, the algorithm proofs presented here suggests general approaches to verification ....

ATTIYA, H., DWORK, C., LYNCH, N. A., AND STOCKMEYER, L. J. 11991), Bounds on the time to reach agreement in the presence of timing uncertainty, in "Proceedings, 23rd ACM Symposium on Theory of Computing," pp. 359-369; also (1990), Technical Memo MIT/LCS/TM-435, Laboratory for Computer Science, MIT.

....and exits via Y0 and obtains the value 0 from the counter A0. Finally, To obtains the value 2 from A0. The behavior is not linearizable because the traversal of the network by T completely precedes T2, yet T2 returns a lower counter value. We use a c c2 timing model in the style of Attiya et al. [5]. Let Cl be the minimum time that it takes for a token to traverse a wire from balancer to balancer, let c2 be the maximum such time, and assume that balancer transitions are instantaneous. This timing model is general enough to capture standard message passing and shared memory balancer ....

H. Attiya, C. Dwork, N. Lynch, L. Stockmeyer, Bounds on the time to reach agreement in the presence of timing uncertainty, J. ACM 41 (1) (1994) 122-152.

....our model with a running time approximately C times the synchronous running time. This simulation strategy is described in Section 3.1. Thus, upper bounds of approximately (f 1)Cd are easily derived. For Byzantine failures, it is not clear how to simulate a synchronous algorithm correctly. In [ADLS90], Attiya, Dwork, Lynch, and Stockmeyer prove nearly tight upper and lower bounds on the time to reach consensus in the presence of stopping failures. Surprisingly, they give a clever algorithm for consensus that runs in time 2fd Cd, much faster than a direct simulation when C is large. They also ....

....recently studied in our model of timing uncertainty include the problem of mutual exclusion ( AL89] and the complexity of a network synchronizer algorithm ( AM90] 1.3 Results of this thesis 1.3. 1 Consensus in the presence of omission failures In Chapter 3, we strengthen the algorithm of [ADLS90] to tolerate omission failures. The resulting algorithm has a running time of 4(f 1)d Cd for n 2f 1. This is approximately within a constant factor (4) of the lower bounds of (f 1)d and (f Gamma 1)d Cd ( ADLS90] and minimizes the dependence on the timing uncertainty C. For n 2f , a more ....

[Article contains additional citation context not shown here]

H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Report TM-435, Laboratory for Computer Science, MIT, November 1990. Also in STOC 1991.

....in a semi synchronous system with n processes, in the presence of late timing failures. Early timing failures, where the steps of a faulty process can occur faster than c 1 , are not addressed here. In the semi synchronous model, late timing failures can be detected by a timeout mechanism [3]: If an expected message from some process is not received within d time units, then that process is known to have failed. By counting its own steps, a process can detect the failure of another process within time approximately c 2 Delta d=c 1 d (see Section 4.1) The ratio c2 c1 is denoted ....

....v then v must be the input of some process. In the synchronous model, exactly f 1 communication rounds are required for reaching consensus in the presence of f crash failures, for any f n [10] In the semisynchronous model, there are algorithms for reaching consensus in the presence of f crash [3] or send omission [17] failures within time O(fd Cd) fd Cd is also a lower bound on the time for reaching consensus in the presence of crash, and hence, send omission failures [3] In contrast, the running time of the best consensus algorithm tolerating Byzantine failures is O(fCd) 17] In ....

[Article contains additional citation context not shown here]

Attiya, H., Dwork, C., Lynch N. A., and Stockmeyer, L. J. Bounds on the time to reach agreement in the presence of timing uncertainty. J. ACM 41, 1 (1994), 122--152.

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H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122-152, 1994.

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H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1):122-152, 1994.

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H. Attiya, C. Dwork, N. A. Lynch and L. J. Stockmeyer, "Bounds on the Time to Reach Agreement in the Presence of Timing Uncertainty," Journal of the ACM, vol. 41, no. 1 (January 1994), pp. 122--152. 37

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H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. J. ACM, 41(1):122--152, Jan. 1994.

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H. Attiya, C. Dwork, N. Lynch, and L. Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. J. ACM, 41(1):122-152, Jan. 1994.

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Hagit Attiya, Cynthia Dwork, Nancy Lynch, and Larry Stockmeyer. Bounds on the time to reach agreement in the presence of timing uncertainty. Journal of the ACM, 41(1), pages 122--152, January 1994.

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