From Binary Consensus to Multivalued Consensus in asynchronous message-passing systems

Mostéfaoui, Achour; Raynal, Michel; Tronel, Frédéric

doi:10.1016/s0020-0190(00)00027-2

Cited by 57 publications

(40 citation statements)

References 8 publications

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“…By contrast, as far as we know, the best construction of a multivalued consensus object from binary consensus objects requires only log(n) base binary consensus objects (e.g., [21]). …”

Section: Resultsmentioning

confidence: 99%

“…In the second phase (lines [11][12][13][14][15][16][17][18][19][20][21][22][23], all the processes that have not decided in the first phase use the vector version binary -simultaneous consensus object to decide on one of the values in these non-empty size 2 snapshots in a way that is consistent with all the decisions that have been already made during the first phase. For each stage of the first phase we associate the smaller value of the size 2 snapshot with 0, and the larger with 1.…”

Section: Constructing a Restricted -Simultaneous Consensus Objectmentioning

confidence: 99%

“…Indeed for k ≥ 2, the scalar version is trivial, since each binary input value can be deter-ministically assigned to a consensus instance. While it is known that the multivalued consensus and the binary consensus are equivalent (e.g., [21]), the same equivalence cannot be achieved in the k-set consensus realm, since it is meaningless to talk about binary k-set consensus. What about k-simultaneous multivalued consensus and k-simultaneous binary consensus?…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The k-simultaneous consensus problem

Afek

Gafni²,

Rajsbaum³

et al. 2009

Distrib. Comput.

Self Cite

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This paper introduces and investigates the ksimultaneous consensus task: each process participates at the same time in k independent consensus instances until it decides in any one of them. It is shown that the k-simultaneous consensus task is equivalent to the kset agreement task in the wait-free read/write shared memory model, and furthermore k-simultaneous consensus possesses properties that k-set does not. In particular we show that the multivalued version and the binary version of the k-simultaneous consensus task are wait-free equivalent. These equivalences are independent of the number of processes. Interestingly, this provides us with a new characterization of the k-set agreement task that is based on the fundamental binary consensus problem.Keywords: Asynchronous shared memory systems, Bi-A preliminary draft of this paper has been presented at the conference ICDCN'06 [3].

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“…By contrast, as far as we know, the best construction of a multivalued consensus object from binary consensus objects requires only log(n) base binary consensus objects (e.g., [21]). …”

Section: Resultsmentioning

confidence: 99%

Section: Constructing a Restricted -Simultaneous Consensus Objectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The k-simultaneous consensus problem

Afek

Gafni²,

Rajsbaum³

et al. 2009

Distrib. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…An alternative approach would be to instead reach agreement over every bit of the initial values, thus reducing the number of instances to log |V |. Similar bit-per-bit approaches that work only for benign failures are used in the reduction algorithms in [50,51].…”

Section: Discussionmentioning

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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“…There are reductions of multi-valued consensus to binary consensus assuming uniform reliable broadcast [13] or randomization [7]. However, because the criterion we consider is convergence to a single value, in which individual agents may change their decisions and do not in general know when convergence has been achieved, we require a somewhat different reduction.…”

Section: Multi-valued Consensusmentioning

confidence: 99%

A Simple Population Protocol for Fast Robust Approximate Majority

Angluin

Aspnes

Eisenstat

Lecture Notes in Computer Science

241

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We describe and analyze a 3-state one-way population protocol to compute approximate majority in the model in which pairs of agents are drawn uniformly at random to interact. Given an initial configuration of x's, y's and blanks that contains at least one non-blank, the goal is for the agents to reach consensus on one of the values x or y. Additionally, the value chosen should be the majority non-blank initial value, provided it exceeds the minority by a sufficient margin. We prove that with high probability n agents reach consensus in O(n log n) interactions and the value chosen is the majority provided that its initial margin is at least ω( √ n log n). This protocol has the additional property of tolerating Byzantine behavior in o( √ n) of the agents, making it the first known population protocol that tolerates Byzantine agents.

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From Binary Consensus to Multivalued Consensus in asynchronous message-passing systems

Cited by 57 publications

References 8 publications

The k-simultaneous consensus problem

The k-simultaneous consensus problem

Consensus in the presence of mortal Byzantine faulty processes

A Simple Population Protocol for Fast Robust Approximate Majority

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