
TL;DR
This paper introduces an early-stabilizing counting algorithm for Byzantine fault-tolerant systems that adapts its stabilization time and bit complexity based on the actual number of faults, improving efficiency.
Contribution
It presents a novel early stabilization approach for counting in Byzantine systems, achieving optimal stabilization time and adaptive bit complexity.
Findings
Stabilizes within asymptotically optimal O(f+1) rounds
Message size is O(log^2 n + log C)
Amortized bit complexity is O(n(f log C + log^2 n))
Abstract
Synchronous Counting is the task of reaching agreement on a common round counter in a synchronous system of nodes with up to Byzantine faults in a self-stabilizing manner. That is, after transient faults may have arbitrarily corrupted the system state and ceased, the at least non-faulty nodes need to (re-)establish that (i) their local outputs are identical and (ii) increase by modulo in each round. An overhead-free reduction from consensus shows that all known lower bounds and impossibilities for consensus carry over to the counting problem. In the other direction, prior work has established that a consensus algorithm can be turned into a counting algorithm at small overhead relative to the running time and bit complexity of , without losing resilience. Taking inspiration from early-stopping consensus protocols, in this work we…
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