In this series of three posts, we discuss two of the most important consensus lower bounds: Lamport, Fischer [1982]: any protocol solving consensus in the synchronous model that is resilient to $t$ crash failures must have an execution with at least $t+1$ rounds. Fischer, Lynch, and Patterson [1983, 1985]: any...| 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
What is the simplest setting where randomization can help solve consensus? Assume lock-step (synchrony) with $f<n$ crash failures. We know that in the worst case reaching agreement takes at least $f+1$ rounds. This lower bound holds even if the protocol is randomized so the natural question is: Can randomization help...| decentralizedthoughts.github.io