Randomized k-set agreement in crash-prone and Byzantine asynchronous systems

Mostéfaoui, Achour; Moumen, Hamouma; Raynal, Michel

doi:10.1016/j.tcs.2017.03.018

Cited by 11 publications

(12 citation statements)

References 19 publications

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“…We check only the high-level algorithm for clean crashes. 4. k-set agreement for crash faults by Mostéfaoui et al [38] (kset), for k = 2. This algorithm works in the presence of clean crashes when n > 3t.…”

Section: Reducing Probabilistic To Non-probabilistic Specificationsmentioning

confidence: 99%

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Verification of randomized consensus algorithms under round-rigid adversaries

Bertrand

Konnov²,

Lazić³

et al. 2021

Int J Softw Tools Technol Transfer

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Randomized fault-tolerant distributed algorithms pose a number of challenges for automated verification: (i) parameterization in the number of processes and faults, (ii) randomized choices and probabilistic properties, and (iii) an unbounded number of asynchronous rounds. This combination makes verification hard. Challenge (i) was recently addressed in the framework of threshold automata. We extend threshold automata to model randomized consensus algorithms that perform an unbounded number of asynchronous rounds. For non-probabilistic properties, we show that it is necessary and sufficient to verify these properties under round-rigid schedules, that is, schedules where processes enter round r only after all processes finished round $$r-1$$ r - 1 . For almost-sure termination, we analyze these algorithms under round-rigid adversaries, that is, fair adversaries that only generate round-rigid schedules. This allows us to do compositional and inductive reasoning that reduces verification of the asynchronous multi-round algorithms to model checking of a one-round threshold automaton. We apply this framework and automatically verify the following classic algorithms: Ben-Or’s and Bracha’s seminal consensus algorithms for crashes and Byzantine faults, 2-set agreement for crash faults, and RS-Bosco for the Byzantine case.

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Section: Reducing Probabilistic To Non-probabilistic Specificationsmentioning

confidence: 99%

“…Using the tool ByMC [24,26], we automatically check the specifications that we derive in Points 1. and 2. and thus verify challenging benchmarks in the parameterized setting. We verify Ben-Or's [4] and Bracha's [11] classic algorithms, and more recent algorithms such as 2-set agreement [38], and RS-Bosco [42].…”

Section: Introductionmentioning

confidence: 99%

Verification of randomized consensus algorithms under round-rigid adversaries

Bertrand

Konnov²,

Lazić³

et al. 2021

Int J Softw Tools Technol Transfer

View full text Add to dashboard Cite

show abstract

“…The difference between the BA problem and the Consensus problem is that every processor has an initial value of its own in the Consensus problem. There are two main types of the Consensus problem, namely the Binary-Valued Consensus (BVC) and the Multi-Valued Consensus (MVC) [22]- [26]. In the BVC problem, the agreement value is either 0 or 1.…”

Section: B Consensus (Binary-valued / Multi-valued)mentioning

confidence: 99%

“…The protocol can decide one of the proposed values or a default value ⊥ / ∈ V . Any protocol designed for the MVC problem shall satisfy five requirements as follows [22], [24], [26]:…”

Section: B Consensus (Binary-valued / Multi-valued)mentioning

confidence: 99%

A Flexible Consensus Protocol for Distributed Systems

Cheng

Tsai

2019

IEEE Access

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This paper presents a new type of Consensus problem named the Consensus (n, m) with alternative plans, where n denotes the total number of processors in the network, m is the number of processors with an initial value, n ≥4 and 1 ≤ m ≤ n. Compared to the traditional Consensus problem, the Consensus (n, m) problem with alternative plans has two major features. First, each processor is no longer required to propose an initial value. It can flexibly choose to propose or not propose an initial value. This feature allows the Consensus problem to be flexibly applied in many new real-world applications of the distributed system. Second, the proposed protocol ensures that all correct processors always agree on a good plan from a correct processor and never on a bad plan. Compared to solutions of the traditional Consensus problem, which does not guarantee that all correct processors agree on a good plan, this feature ensures the rationality of the Consensus value. In other words, by solving the Consensus (n, m) problem with alternative plans, the fault tolerance and reliability of distributed systems can be improved.

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“…In this paper, we extend this idea to randomized distributed algorithms and probabilistic properties [4,16,2]. Rather than arguing on traces, probabilistic guarantees require us to reason on Markov decision processes (MDPs).…”

Section: Introductionmentioning

confidence: 99%

A Reduction Theorem for Randomized Distributed Algorithms Under Weak Adversaries

Bertrand

Lazić

Widder³

2021

Lecture Notes in Computer Science

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Weak adversaries are a way to model the uncertainty due to asynchrony in randomized distributed algorithms. They are a standard notion in correctness proofs for distributed algorithms, and express the property that the adversary (scheduler), which has to decide which messages to deliver to which process, has no means of inferring the outcome of random choices, and the content of the messages. In this paper, we introduce a model for randomized distributed algorithms that allows us to formalize the notion of weak adversaries. It applies to randomized distributed algorithms that proceed in rounds and are tolerant to process failures. For this wide class of algorithms, we prove that for verification purposes, the class of weak adversaries can be restricted to simple ones, so-called round-rigid adversaries, that keep the processes tightly synchronized. As recently a verification method for round-rigid adversaries has been introduced, our new reduction theorem paves the way to the parameterized verification of randomized distributed algorithms under the more realistic weak adversaries.

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Randomized k-set agreement in crash-prone and Byzantine asynchronous systems

Cited by 11 publications

References 19 publications

Verification of randomized consensus algorithms under round-rigid adversaries

Verification of randomized consensus algorithms under round-rigid adversaries

A Flexible Consensus Protocol for Distributed Systems

A Reduction Theorem for Randomized Distributed Algorithms Under Weak Adversaries

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