A combinatorial characterization of the distributed tasks which are solvable in the presence of one faulty processor

Biran, Ofer; Moran, Shlomo; Zaks, Shmuel

doi:10.1145/62546.62590

Cited by 52 publications

(22 citation statements)

References 9 publications

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“…Since X is deterministic, there is a protocol that brings X to state s. We use this observation to derive a protocol that solves another variant of consensus, named team consensus [14,15], which implies that the protocol also solves consensus [3,15]. (2) We show that this is not the case with non-deterministic types. Basically, we exhibit a new non-deterministic type, which we call rambler, that implements weak consensus for an arbitrary number of processes, but cannot implement consensus even among two processes.…”

Section: Contributionsmentioning

confidence: 94%

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The gap in circumventing the impossibility of consensus

Guerraoui

Kuznetsov

2008

Journal of Computer and System Sciences

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The impossibility of reaching deterministic consensus in an asynchronous and crash prone system was established for a weak variant of the problem, usually called weak consensus, where a set of processes need to decide on a common value in {0, 1}, so that both 0 and 1 are possible decision values. On the other hand, approaches to circumventing the impossibility focused on a stronger variant of the problem, called consensus, where the processes need to decide on one of the values they initially propose (0 or 1). This paper studies the computational gap between the two problems. We show that any set of deterministic object types that, combined with registers, implements weak consensus, also implements consensus. Then we exhibit a non-deterministic type that implements weak consensus, among any number of processes, but, combined with registers, cannot implement consensus even among two processes. In modern terminology, this type has consensus power 1 and weak consensus power ∞.

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Section: Contributionsmentioning

confidence: 94%

“…We call the local state of p i just after the decision the final state of p i . Similar to [2,3,7], we define the decision graph of P [13], denoted by C(P ), as follows. Vertices of C(P ) represent the final states of processes p 0 and p 1 resulting from all possible executions of P (for all possible initial states).…”

Section: Weak Consensus With Ramblermentioning

confidence: 99%

The gap in circumventing the impossibility of consensus

Guerraoui

Kuznetsov

2008

Journal of Computer and System Sciences

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“…The work in [FLP85] proves the nonexistence of a consensus protocols that can tolerate a single crash failure, for a completely asynchronous message passing system. Various extensions of this fundamental result, also for a single crash failure, prove the impossibility of other problems in the same model [MW87,Tau87,BMZ88]. Other works study the possibility of solving variety of problems in asynchronous systems with numerous crash failures, and in several message passing models [ABD + 87, BW87, DDS87, DLS88, TKM89a].…”

Section: Related Workmentioning

confidence: 96%

Possibility and impossibility results in a shared memory environment

Taubenfeld

Moran

1996

Acta Informatica

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We focus on unreliable asynchronous shared memory model which support only atomic read and write operations. For such a model we provide a necessary condition for the solvability of problems in the presence of multiple undetectable crash failures. Also, by using game-theoretical notions, a necessary and sufficient condition is provided, for the solvability of problems in the presence of multiple undetectable initial failures (i.e., processes may fail only prior to the execution).Our results imply that many problems such as consensus, choosing a leader, ranking, matching and sorting are unsolvable in the presence of a single crash failure, and that variants of these problems are solvable in the presence of t − 1 crash failures but not in the presence of t crash failures.We show that a shared memory model can simulate various message passing models, and hence our impossibility results hold also for those message passing models. Our results extend and generalize previously known impossibility results for various asynchronous models.

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“…Why not build a decision program whose input is a task encoding and whose output is "yes" or "no" according to whether the encoded task is r/w wait-free solvable or not? Indeed this question was raised in [14] where they show that 2 processors tasks is a reachability problem and consequently, decidable.…”

Section: -Resilient Tasks Are Undecidablementioning

confidence: 99%

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

Gafni

2009

Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing

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A distributed task T on n processors is an input/output relation between a collection of processors' inputs and outputs. While all tasks are solvable if no processor may ever crash, the FLP result revealed that the possibility of a failure of just a single processor precludes a solution to the task of consensus. That is consensus is not solvable 1-resiliently. Yet, some nontrivial tasks are wait-free solvable, i.e. n − 1-resiliently. What tasks are solvable if at most t < n processors may crash? I.e. what tasks are solvable t-resiliently?The Herlihy-Shavit condition characterizes wait-free solvability, i.e., when t = n − 1. The Borowsky-Gafni (BG) simulation extends this characterization to the t-resilient case for the case "colorless" tasks -tasks like consensus in which one processor can adopt the output of any other processor. It does this by reducing questions about t-resilient solvability, to a question of wait-free solvability. The latter question has been characterized.In this paper, we amend the BG-simulation to result in the Extended-BG-simulation, an extension that yields a full characterization of t-resilient solvability: A task T on n processors is solvable t-resiliently iff all tasks T on t + 1 simulators s0, . . . , st created as follows are wait-free solvable. Simulator si is given an input of processor pi as well as the input to a set of processors of size n − (t + 1) with ids higher than i. Simulator si outputs for pi as well as for a (possibly different) set of processors of size n − (t + 1) with ids higher than i. The input/output of the t + 1 simulators have to be a projection of a single original input/output tuple-pair in T .We demonstrate the convenience that the characterization provides, in two ways. First, we prove a new equivalence result: We show that n processes can solve t-resiliently weak renaming with n + (t + 1) − 2 names, where n > 1 and 0 < t < n, iff weak-renaming on t + 1 processors is wait-free solvable with 2t names. Second, we reproduce the result that the solvability of n-processors tasks, t-resiliently, for t > 1 and n > 2, is undecidable, by a simple reduction to

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A combinatorial characterization of the distributed tasks which are solvable in the presence of one faulty processor

Cited by 52 publications

References 9 publications

The gap in circumventing the impossibility of consensus

The gap in circumventing the impossibility of consensus

Possibility and impossibility results in a shared memory environment

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

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