In this third post, we conclude with the celebrated Fischer, Lynch, and Paterson impossibility result from 1985. It is the fundamental lower bound for consensus in the asynchronous model. Theorem 1 (FLP85): Any protocol $\mathcal{P}$ solving consensus in the asynchronous model that is resilient to even just one crash failure...| decentralizedthoughts.github.io
In this second post, we show the fundamental lower bound on the number of rounds for consensus protocols in the synchronous model. Theorem: Any protocol solving consensus in the synchronous model for $n$ parties that is resilient to $n-2 \geq t \geq 1$ crash failures must have an execution with...| decentralizedthoughts.github.io
The prevailing view on fault-tolerant agreement is that it is impossible in asynchrony for deterministic protocols, but adding randomization solves the problem. This statement is confusing in two aspects: The FLP result says that any protocol, even a randomized protocol, must have a non-terminating execution where every configuration is bivalent...| decentralizedthoughts.github.io
Many systems try to optimize executions that are failure free. If we absolutely knew that there will be no failures, parties could simply send each other messages with our inputs and reach consensus by outputting, say, the majority value. Thus completing the protocol after one round. What happens if there...| decentralizedthoughts.github.io
