From 0cfe951ca90f2d8c050e2d900bb4c9b0b6793443 Mon Sep 17 00:00:00 2001 From: Jeff Burdges Date: Tue, 16 Apr 2019 12:24:27 +0200 Subject: [PATCH] Al's comments from discussion --- pdf/grandpa.tex | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex index 34c34e8..05e20af 100644 --- a/pdf/grandpa.tex +++ b/pdf/grandpa.tex @@ -277,10 +277,14 @@ In addition to a set of voters for each of the two votes in a round, we assume t We let $V_{r,v}$ and $C_{r,v}$ be the sets of prevotes and precommits respectively received by $v$ from round $r$ at the current time. -We define $E_{r,v}$ to be $v$'s estimate of what might have been finalised in round $r$ given by the last block in the chain with head $g(V_{r,v})$ for which it is possible for $C_{r,r}$ to have a supermajority. Next we define a condition which will allow us to dafely conclude that $E_{r,v} \geq B$ for all $B$ that might be finalised in round $r$: -If either $E_{r,v} < g(V_{r,v})$ or it is impossible for $C_{r,v}$ to have a supermajority for any children of $g(V_{r,v})$, then we say that {\em $v$ sees that round $r$ is completable}. $E_{0,v}$ is the genesis block, assuming we start at $r=1$. +We define $E_{r,v}$ to be $v$'s estimate of what might have been finalised in round $r$, given by the last block in the chain with head $g(V_{r,v})$ for which it is possible for $C_{r,r}$ to have a supermajority. Next we define a condition which will allow us to safely conclude that $E_{r,v} \geq B$ for all $B$ that might be finalised in round $r$: +If either $E_{r,v} < g(V_{r,v})$ or it is impossible for $C_{r,v}$ to have a supermajority for any children of $g(V_{r,v})$, then we say that {\em $v$ sees that round $r$ is completable}. $E_{0,v}$ is the genesis block, assuming we start at $r=1$. -We have a time bound $T$ that we hope suffices to send messages and gossip them to everyone. +In other words, a round $r$ is completable when our estimate chain $E_{r,v}$ contains everything that could have been finalised in round $r$, which makes it possible to begin the next round $r+1$. + +We have a time bound $T$ that we hope suffices to send messages and gossip them to everyone. +Inside a round, the properties both of $E_{r,v}$ having a supermajority, meaning $E_{r,v} < g(V_{r,v})$, as well as of it being imposible to have a supermajority for some given block are monotone, so the property of being completable is monotone as well. +We therefore expect that, if anyone anyone sees a round is completable, then everyone will see this within time $T$. In round $r$ an honest participant $v$ does the following: