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13
The weakest failure detector for message passing set-agreement
- In DISC
, 2008
"... Abstract. In the set-agreement problem, n processes seek to agree on at most n−1 different values. This paper determines the weakest failure detector to solve this problem in a message-passing system where processes may fail by crashing. This failure detector, called the Loneliness detector and deno ..."
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Abstract. In the set-agreement problem, n processes seek to agree on at most n−1 different values. This paper determines the weakest failure detector to solve this problem in a message-passing system where processes may fail by crashing. This failure detector, called the Loneliness detector and denoted L, outputs one of two values, “true ” or “false ” such that: (1) there is at least one process where L outputs always “false”, and(2) if only one process is correct, L eventually outputs “true ” at this process.
On failure detectors and type boosters
- In Proceedings of the 17th International Symposium on Distributed Computing (DISC’03
, 2003
"... Abstract. The power of an object type T can be measured as the maximum number n of processes that can solve consensus using only objects of T and registers. This number, denoted cons(T), is called the consensus power of T. This paper addresses the question of the weakest failure detector to solve co ..."
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Cited by 12 (4 self)
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Abstract. The power of an object type T can be measured as the maximum number n of processes that can solve consensus using only objects of T and registers. This number, denoted cons(T), is called the consensus power of T. This paper addresses the question of the weakest failure detector to solve consensus among a number k> n of processes that communicate using shared objects of a type T with consensus power n. In other words, we seek for a failure detector that is sufficient and necessary to “boost ” the consensus power of a type T from n to k. It was shown in [21] that a certain failure detector, denoted Ωn, is sufficient to boost the power of a type T from n to k, and it was conjectured that Ωn was also necessary. In this paper, we prove this conjecture for one-shot deterministic types. We show that, for any one-shot deterministic type T with cons(T) ≤ n, Ωn is necessary to boost the power of T from n to any k> n. Our result generalizes, in a precise sense, the result of the weakest failure detector to solve consensus in asynchronous message-passing systems [6]. As a corollary of our result, we show that Ωn is the weakest failure detector to boost the resilience of a system of (n − 1)-resilient objects of any types and wait-free registers with respect to the consensus problem. 1
Weakening failure detectors for k-set agreement via the approach
- In Proceedings of DISC
, 2007
"... Abstract. In this paper, we propose the partition approach and define several new classes of partitioned failure detectors weaker than existing failure detectors for the k-set agreement problem in both the shared-memory model and the message-passing model. In the shared-memory model with n + 1 proce ..."
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Abstract. In this paper, we propose the partition approach and define several new classes of partitioned failure detectors weaker than existing failure detectors for the k-set agreement problem in both the shared-memory model and the message-passing model. In the shared-memory model with n + 1 processes, for any 2 ≤ k ≤ n, we first propose a partitioned failure detector ΠΩk that solves k-set agreement with shared read/write registers and is strictly weaker than Ωk, which was conjectured to be the weakest failure detector for k-set agreement in the shared-memory model [19]. We then propose a series of partitioned failure detectors that can solve n-set agreement, yet they are strictly weaker than Υ [10], the weakest failure detector ever found before our work to circumvent any asynchronous impossible problems in the shared-memory model. We also define two new families of partitioned failure detectors in the message-passing model that are strictly weaker than the existing ones for k-set agreement. Our results demonstrate that the partition approach opens a new dimension for weakening failure detectors related to set agreement, and it is an effective approach to check whether a failure detector is the weakest one or not for set agreement. So far, all previous candidates for the weakest failure detectors of set agreement have been disproved by the partitioned failure detectors.
Failure Detectors to Solve Asynchronous k-Set Agreement: a Glimpse of Recent Results
"... Abstract: In the k-set agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process ..."
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Abstract: In the k-set agreement problem, each process proposes a value and has to decide a value in such a way that a decided value is a proposed value and at most k different values are decided. This problem can easily be solved in synchronous systems or in asynchronous systems prone to t process crashes when t < k. In contrast, it has been shown that k-set agreement cannot be solved in asynchronous systems when k ≤ t. Hence, since several years, the failure detector-based approach has been investigated to circumvent this impossibility. This approach consists in enriching the underlying asynchronous system with an additional module per process that provides it with information on failures. Hence, without becoming synchronous, the enriched system is no longer fully asynchronous. This paper surveys this approach in both asynchronous shared memory systems and asynchronous message passing systems. It presents and discusses recent results and associated k-set agreement algorithms.
Sharing is harder than agreeing
- IN: PODC 2008: PROCEEDINGS OF THE TWENTY-SEVENTH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 2008
"... One of the most celebrated results of the theory of distributed computing is the impossibility, in an asynchronous system of n processes that communicate through shared memory registers, to solve the set agreement problem where the processes need to decide on up to n − 1 among their n initial values ..."
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One of the most celebrated results of the theory of distributed computing is the impossibility, in an asynchronous system of n processes that communicate through shared memory registers, to solve the set agreement problem where the processes need to decide on up to n − 1 among their n initial values. In short, the result indicates that the register abstraction is too weak to implement the set agreement one. This paper explores the relation between these abstractions in a message passing system where a register is not a given physical device but is rather itself implemented by processes communicating through message passing. We show that, maybe surprisingly, the information about process failures that is necessary and sufficient to implement a register shared by two particular processes is sufficient but not necessary to implement set agreement. We later generalize this result by considering k-set agreement, where the processes can decide on up to k values, and comparing it with a register shared by any particular subset of 2k processes. We prove that, for 1 ≤ k ≤ n/2, (a) any failure information that is sufficient to implement a register shared by 2k processes is sufficient to implement (n − k)-set agreement but (b) a failure information that is sufficient for (n − k)-set agreement is not sufficient for a register shared by 2k processes. We also prove that (c) a failure information that is sufficient for a register shared by 2k processes is not sufficient for ((n-k)-1)-set agreement.
Free-for-All Execution: Unifying Resiliency, Set-Consensus, and Concurrency
, 2008
"... This paper proposes a free-for-all execution scheme for read-write code, whether wait-free, t-resilient, or one that utilizes set-consensus. It employs two new novel simulating techniques: Extended-BG-Simulation, and Simulation-by-Value. Its architecture consists of 3 layers: At the bottom, real pro ..."
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This paper proposes a free-for-all execution scheme for read-write code, whether wait-free, t-resilient, or one that utilizes set-consensus. It employs two new novel simulating techniques: Extended-BG-Simulation, and Simulation-by-Value. Its architecture consists of 3 layers: At the bottom, real processors just signal their participation, at the middle layer, virtual Extended-BG-simulators execute the active codes free-for-all, and at the top layer, the original processors cooperatively use Simulation-by-Value to simulate the virtual BG-simulators. The Extended-BG-simulation removes a drawback from the BG-simulation. In the BGsimulation each simulator may be interested in the output of a particular code, but the simulation guarantees an output of some code, rather than a specific one. The modified simulation removes this drawback. The Simulation-by-Value which subsumes the BG-simulation, allows us to show that if in run-time disagreement happens at some point to be low it can be kept that way afterwards. The combination of the two simulations allows for a clean separation of concerns. It is the BG-simulators which are programmed to decide which original code to execute next among all active codes. The processors just pick-up BG-simulators that will progress, from a prefix of an ordered sequence of possibly infinite simulators, with all the rest effectively faulty. Besides many interesting ramifications of the new execution scheme, the most important ones are that: The use of k-Set Consensus is tantamount to k-concurrency, while resiliency is wait-free with some level of “synchrony ” just at the first step.
(anti−Ω x × Σz)-based k-set Agreement Algorithms
, 2010
"... This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω k and the weak-quor ..."
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This paper considers the k-set agreement problem in a crash-prone asynchronous message passing system enriched with failure detectors. Two classes of failure detectors have been previously identified as necessary to solve asynchronous k-set agreement: the class anti-leader anti−Ω k and the weak-quorum class Σk. The paper investigates the families of failure detector (anti−Ω x)1≤x≤n and (Σz)1≤z≤n. It characterizes in an n processes system equipped with failure detectors anti−Ω x and Σz for which values of k,x and z k-set-agreement can be solved. While doing so, the paper (1) disproves previous conjunctures about the weakest failure detector to solve k-set-agreement in the asynchronous message passing model and, (2) introduces the first indulgent algorithm that tolerates a majority of processes failures.
The disagreement power of an adversary: extended abstract
- In PODC 2009, ACM
"... At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes f ..."
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At the heart of distributed computing lies the fundamental result that the level of agreement that can be obtained in an asynchronous shared memory model where t processes can crash is exactly t + 1. In other words, an adversary that can crash any subset of size at most t can prevent the processes from agreeing on t values. But what about the rest (22 n−n) adversaries that might crash certain combination of processes and not others? This paper presents a precise way to characterize such ad-versaries by introducing the notion of disagreement power: the biggest integer k for which the adversary can prevent processes from agreeing on k values. We show how to com-pute the disagreement power of an adversary and how this notion enables to derive n classes of adversaries. We use our characterization to also close the question of the weakest failure detector for k-set agreement. So far, the result has been obtained for two extreme cases: consensus and n−1-set agreement. We answer this question for any k.
