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...nsus can be solved without stable storage using ⋄Se. B. Implementation of ⋄Se and ⋄S ′ e in partially synchronous systems We show how to implement ⋄Se and ⋄S ′ e in the models of partial synchrony of =-=[5,3]-=- (extended to systems with crashes and recoveries). [5] considers two models of partial synchrony. Roughly speaking, the first model, denoted M1 here, stipulates that in every execution there are boun...

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...eement: Good processes do not decide different values. • Termination: If all good processes propose a value, then they all eventually decide. A stronger version of consensus, called uniform consensus =-=[9]-=-, requires: • Uniform Agreement: Processes do not decide different values. The above specification allows a process to decide more than once. However, with Agreement, a good process cannot decide two ...

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...esses: each process can then do the counting and deciding by itself (this takes one δ and O(n 2 ) messages). 8.2 Quiescence An algorithm is quiescent if eventually all processes stop sending messages =-=[1]-=-. It is clear that no consensus algorithm can be quiescent in the presence of unstable processes (each time such a process recovers, it must be sent the decision value, at which point it may crash aga...

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...stems – Stable storage 1 Introduction The problem of solving consensus in asynchronous systems with unreliable failure detectors (i.e., failure detectors that make mistakes) was first investigated in =-=[3,2]-=-. But these works only considered systems where process crashes are permanent and links are reliable (i.e., they do not lose messages). In real systems, however, processes may recover after crashing a...

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...has received (k, sp, ∗, report); • Rp, the value of set Rp. 15 The Fair Loss and Per-Message Fair Loss properties of links are called Weak Loss Limitation and Strong Loss Limitation, respectively, in =-=[8]-=-. Clearly, to show that RV p[k] ∩ RV q[k] �= ∅, itissufficient to show that Pp ∩ Pq �= ∅. We first claim that (1) processes in Rp crash before p starts sending (k, sp, report, request) to any process ...

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... one. To deal with the message loss problem, each process p has a task retransmit that periodically retransmits the last message sent to each process (only the last message really matters, just as in =-=[4,6,7]-=-). This task is terminated once p decides. We now describe the algorithm in more detail. When a process recovers from a crash, it stops participating in the algorithm, except that it periodically broa...

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...ction and consensus in the crash-recovery model 101 1.3 Related work The problem of solving consensus with failure detectors in systems where processes may recover from crashes was first addressed in =-=[4]-=- (with crash-recovery as a form of omission failures) and more recently studied in [10,7]. In [4,10,7], the question of whether stable storage is always necessary is not addressed, and all the algorit...

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...stems – Stable storage 1 Introduction The problem of solving consensus in asynchronous systems with unreliable failure detectors (i.e., failure detectors that make mistakes) was first investigated in =-=[3,2]-=-. But these works only considered systems where process crashes are permanent and links are reliable (i.e., they do not lose messages). In real systems, however, processes may recover after crashing a...

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... however, processes may recover after crashing and links may lose messages. In this paper, we focus on solving consensus with failure detectors in such systems, a problem that was first considered in =-=[4,10,7]-=- (a brief comparison with these works is in Sect. 1.3). Solving consensus in a system where process may recover after crashing raises two new problems; one regards the need for stable storage and the ...

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... however, processes may recover after crashing and links may lose messages. In this paper, we focus on solving consensus with failure detectors in such systems, a problem that was first considered in =-=[4,10,7]-=- (a brief comparison with these works is in Sect. 1.3). Solving consensus in a system where process may recover after crashing raises two new problems; one regards the need for stable storage and the ...