The extended BG-simulation and the characterization of t-resiliency

Gafni, Eli

doi:10.1145/1536414.1536428

Cited by 38 publications

(77 citation statements)

References 16 publications

(27 reference statements)

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“…Basically, for a particular class of decision tasks called colorless tasks (those are the tasks where, if a process decides a value, any other process is allowed to decide the very same value), BG simulation characterizes t-resilience in terms of wait-freedom. (The BG simulation algorithm has been extended to colored tasks in [17,24]). As an example, let us assume that A solves consensus, despite up to t = 1 crash, among n processes in a read/write shared memory system.…”

Section: Context Of the Workmentioning

confidence: 99%

The multiplicative power of consensus numbers

Imbs

Raynal

2010

Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

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The Borowsky-Gafni (BG) simulation algorithm is a powerful reduction algorithm that shows that t-resilience of decision tasks can be fully characterized in terms of wait-freedom. Said in another way, the BG simulation shows that the crucial parameter is not the number n of processes but the upper bound t on the number of processes that are allowed to crash. The BG algorithm considers colorless decision tasks in the base read/write shared memory model. (Colorless means that if, a process decides a value, any other process is allowed to decide the very same value.) This paper considers system models made up of n processes prone to up to t crashes, and where the processes communicate by accessing read/write atomic registers (as assumed by the BG) and (differently from the BG) objects with consensus number x, accessible by at most x processes (with x ≤ t < n). Let ASM (n, t, x) denote such a system model. While the BG simulation has shown that the models ASM (n, t, 1) and ASM (t + 1, t, 1) are equivalent, this paper focuses the pair (t, x) of parameters of a system model. Its main result is the following: the system models ASM (n 1 , t 1 , x 1 ) and ASM (n 2 , t 2 , x 2 ) have the same computational power for colorless decision tasks if and only if t1 x1 = t2 x2 . As can be seen, this contribution complements and extends the BG simulation. It shows that consensus numbers have a multiplicative power with respect to failures, namely the system models ASM (n, t , x) and ASM (n, t, 1) are equivalent for colorless decision tasks iff (t × x) ≤ t ≤ (t × x) + (x − 1).Key-words: Asynchronous processes, BG simulation, Consensus number, Distributed computability, Fault-Tolerance, Process crash failure, Reduction algorithm, t-Resilience, k-Set agreement, Shared memory system, Synchronization power, System model, Waitfreedom. La puissance multiplicative des nombres de consensusRésumé : Ce rapportétudie la puissance multiplicative des nombres de consensus par rapport au nombre de fautes.

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Section: Context Of the Workmentioning

confidence: 99%

The multiplicative power of consensus numbers

Imbs

Raynal

2010

Proceedings of the 29th ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing

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“…Our technique allows us to characterize the complexity of set agreement in partially synchronous systems, as well as to refine earlier lower bounds for early-deciding synchronous set agreement. One direction of future work is to extend our lower bound results to other tasks by encapsulating the Extended BG simulation [11]. On the algorithmic side, the solvability of set agreement in partially synchronous systems without a majority of correct processes remains an open question.…”

Section: Resultsmentioning

confidence: 99%

“…In every round, each process broadcasts its entire state (line 5), and receives all the messages for the current round (line 6), updating its view of which processes have failed and which rounds are synchronous (lines 7-10). A process decides if it receives a message from another process that has already decided (lines [11][12] Fig. 2.…”

Section: Descriptionmentioning

confidence: 99%

Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement

Alistarh

Gilbert

Guerraoui

et al. 2009

Algorithms and Computation

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Abstract. Set agreement is a fundamental problem in distributed computing in which processes collectively choose a small subset of values from a larger set of proposals. The impossibility of fault-tolerant set agreement in asynchronous networks is one of the seminal results in distributed computing. The complexity of set agreement in synchronous networks has also been a significant research challenge. Real systems, however, are neither purely synchronous nor purely asynchronous. Rather, they tend to alternate between periods of synchrony and periods of asynchrony.In this paper, we analyze the complexity of set agreement in a such a "partially synchronous" setting, presenting the first (asymptotically) tight bound on the complexity of set agreement in such systems. We introduce a novel technique for simulating, in faultprone asynchronous shared memory, executions of an asynchronous and failure-prone message-passing system in which some fragments appear synchronous to some processes. We use this technique to derive a lower bound on the round complexity of set agreement in a partially synchronous system by a reduction from asynchronous wait-free set agreement. We also present an asymptotically matching algorithm that relies on a distributed asynchrony detection mechanism to decide as soon as possible during periods of synchrony.By relating environments with differing degrees of synchrony, our simulation technique is of independent interest. In particular, it allows us to obtain a new lower bound on the complexity of early deciding k-set agreement complementary to that of [12], and to re-derive the combinatorial topology lower bound of [13] in an algorithmic way.

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“…In fact, (n + t − 1) is the best achievable namespace size when t processes may crash [Castañeda and Rajsbaum 2010], [Castañeda and Rajsbaum 2012]. The proof of this result required the use of complex techniques [Herlihy and Shavit 1999], [Gafni 2009]. This impossibility result can be circumvented through the use of randomization: there exist randomized renaming algorithms that ensure a tight namespace of n names, guaranteeing name uniqueness in all executions and termination with probability 1, e.g.…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds for Asynchronous Renaming

Alistarh

Aspnes

Censor-Hillel

et al. 2014

J. ACM

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This paper presents the first tight bounds on the time complexity of shared-memory renaming, a fundamental problem in distributed computing in which a set of processes need to pick distinct identifiers from a small namespace.We first prove an individual lower bound of Ω(k) process steps for deterministic renaming into any namespace of size sub-exponential in k, where k is the number of participants. The bound is tight: it draws an exponential separation between deterministic and randomized solutions, and implies new tight bounds for deterministic concurrent fetch-and-increment counters, queues and stacks. The proof is based on a new reduction from renaming to another fundamental problem in distributed computing: mutual exclusion. We complement this individual bound with a global lower bound of Ω(k log(k/c)) on the total step complexity of renaming into a namespace of size ck, for any c ≥ 1. This result applies to randomized algorithms against a strong adversary, and helps derive new global lower bounds for randomized approximate counter implementations, that are tight within logarithmic factors.On the algorithmic side, we give a protocol that transforms any sorting network into a randomized strong adaptive renaming algorithm, with expected cost equal to the depth of the sorting network. This gives a tight adaptive renaming algorithm with expected step complexity O(log k), where k is the contention in the current execution. This algorithm is the first to achieve sublinear time, and it is time-optimal as per our randomized lower bound. Finally, we use this renaming protocol to build monotone-consistent counters with logarithmic step complexity and linearizable fetch-and-increment registers with polylogarithmic cost.

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The extended BG-simulation and the characterization of t-resiliency

Cited by 38 publications

References 16 publications

The multiplicative power of consensus numbers

The multiplicative power of consensus numbers

Of Choices, Failures and Asynchrony: The Many Faces of Set Agreement

Tight Bounds for Asynchronous Renaming

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