🤖 AI Summary
This work resolves the theoretical tension between the feasibility of deterministic crash-tolerant consensus in fully asynchronous settings and the FLP impossibility result. By constructing a rigorous formal framework, it demonstrates that the apparent contradiction between Attia et al.’s conclusions and alternative claims of consensus possibility stems from differing assumptions about the semantics of protocol rounds. Building on this insight, the paper introduces a novel multi-crash-tolerant consensus algorithm. It provides the first formal proof that bridges a critical gap in asynchronous consensus theory, establishing the theoretical feasibility of achieving deterministic consensus tolerating multiple crashes within a fully asynchronous model, accompanied by a complete correctness proof of the proposed algorithm.
📝 Abstract
In this paper, we resolve the apparent contradiction between the proven possibility of deterministic crash-tolerant consensus in a fully asynchronous environment and the reconfirmation of the FLP impossibility result by Attiya, Castañeda, and Rajsbaum. With the use of a strictly formal framework that extends their reasoning, we close this fundamental gap in theory. Specifically, we demonstrate that a single protocol phase separates their findings from reaching the exact opposite conclusion. Another important outcome is a novel algorithm with ability to tolerate multiple crash faults. We provide a rigorous, strictly formal proof of correctness to validate our results.