New hybrid fault models for asynchronous approximate agreement

Azadmanesh, M. H.; Kieckhafer, R. M.

doi:10.1109/12.494101

Cited by 24 publications

(19 citation statements)

References 21 publications

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“…2 Lemma 2.5 (Lipschitz condition for µ). The FTI intersection function F satisfies the Lipschitz condition for the uniform metric µ, which means that for any δ > 0 and any two sets 1 Note carefully that we used the alternative notation M n−f n in [12], which is equal to M f n in this paper. 2 Since we will primarily consider the uniform metric in our paper, the phrase "the Lipschitz condition" usually assumes this kind of metric.…”

Section: Item (3) Of Lemma 24 Implies That One Should Always Trymentioning

confidence: 99%

How to reconcile fault-tolerant interval intersection with the Lipschitz condition

Schmid

Schossmaier

2001

Distrib Comput

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We present a new fault-tolerant intersection function F , which satisfies the Lipschitz condition for the uniform metric and is optimal among all functions with this property. F thus settles Lamport's question about such a function raised in [5]. Our comprehensive analysis reveals that F has exactly the same worst-case performance as the optimal Marzullo function M, which does not satisfy a Lipschitz condition. The utilized modelling approach in conjunction with a powerful hybrid fault model ensures compatibility of our results with any known application framework, including replicated sensors and clock synchronization.Key words: Fault-tolerant interval intersection -Marzullo function -Hybrid fault models -Interval-based clock synchronization MotivationConsider some quantity like a point in real-time (for clock synchronization) or a temperature value (for replicated sensors) that is not known exactly but only within some range. Such a quantity t can be represented by a real interval I = [x, y] containing t, which makes the uncertainty explicit by its length |I| = y −x. Now suppose that we are somehow provided with n ≥ 1 different intervals I = {I 1 , . . . , I n } all representing the same t, and that we want to extract a single interval of minimum length that contains t. If all input intervals are accurate (i.e. non-faulty), in the sense that t ∈ I i , 1 ≤ i ≤ n, it is obvious that J = n i=1 I i contains t and hence J = ∅. In fact, J is the best (deterministic) information about t that can be deduced from I.However, the question arises what to do if some of the input intervals are not accurate (i.e. faulty), that is, t ∈

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Section: Item (3) Of Lemma 24 Implies That One Should Always Trymentioning

confidence: 99%

How to reconcile fault-tolerant interval intersection with the Lipschitz condition

Schmid

Schossmaier

2001

Distrib Comput

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“…Our crash faults are more severe than the (systemwide consistently perceived) benign faults of [AK96], since it cannot be decided locally whether an omissive interval belongs to a crash fault or to an (inconsistent) receive omission. However, it is of course possible to "merge" crash and symmetric faults, in the sense that the former are counted in f s respectively f s and f c = f c = 0 (note that n p − f p = n − f s − f a in this case).…”

Section: Lemma 4 (Precisionmentioning

confidence: 99%

“…For our precision analysis, the single-interval faults of Definition 4 must be complemented by faults of pairs of intervals I s p and I s q obtained at nodes p and q, respectively, in the broadcast from a single node s. Different classes of faults (crash/symmetric/asymmetric) will be introduced to facilitate a hybrid fault model , (refer to [AK96], [WS00]). It will allow us to exploit the fact that masking f symmetric faults with OA requires only n ≥ 2f + 1, whereas n ≥ 3f + 1 is needed if all faults are asymmetric ones ( [DHS86]).…”

Section: Fault Modelmentioning

confidence: 99%

Untitled

Schmid¹

2000

Chicago J. of Theoretical Comp. Sci.

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“…Proof By lines [31][32][33][34][35][36][37] it follows obviously that a value must be in the set acceptable p of a correct process p in order to be decided upon. Initially, only the initial value of p is in acceptable p and only values broadcast by at least t + 1 processes, i.e., by at least one correct process, are added.…”

Section: Theorem 9 (Validity) If a Correct Process Decides On Some Vamentioning

confidence: 99%

“…Another approach was to augment the asynchronous system with failure detectors [10,26,27]. Other approaches aim at optimizing normal case behavior [28][29][30] or consider more elaborate fault models in an effort to improve fault resilience as, for instance, Byzantine faults with recovery [31,32] or hybrid failure models [33][34][35].…”

Section: Related Workmentioning

confidence: 99%

Consensus in the presence of mortal Byzantine faulty processes

et al. 2011

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We consider the problem of reaching agreement in distributed systems in which some processes may deviate from their prescribed behavior before they eventually crash. We call this failure model "mortal Byzantine". After discussing some application examples where this model is justified, we provide matching upper and lower bounds on the number of faulty processes, and on the required number of rounds in synchronous systems. We then continue our study by varying different system parameters. On the one hand, we consider the failure model under weaker timing assumptions, namely for partially synchronous systems and asynchronous systems with unreliable failure detectors. On the other hand, we vary the failure model in that we limit the occurrences of faulty steps that actually lead to a crash in synchronous systems.

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New hybrid fault models for asynchronous approximate agreement

Cited by 24 publications

References 21 publications

How to reconcile fault-tolerant interval intersection with the Lipschitz condition

How to reconcile fault-tolerant interval intersection with the Lipschitz condition

Untitled

Consensus in the presence of mortal Byzantine faulty processes

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