From e2e12ecd50cddae2229703305f7ea7c231a8aa53 Mon Sep 17 00:00:00 2001 From: Jeff Burdges Date: Wed, 7 Nov 2018 14:44:01 +0100 Subject: [PATCH] Avoid e.g. followed by i.e --- pdf/grandpa.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex index 910368e..ce06599 100644 --- a/pdf/grandpa.tex +++ b/pdf/grandpa.tex @@ -42,8 +42,8 @@ We present a finality gadget that works in a partially synchronous network model \subsection{Formalising the problem} -We need to incorporate into the definition of Byzantine agreement that we have access to a protocol that would achieve eventual consensus if we did not affect it. Consider a typical definition of a multi-values Byzantine agreement. -We have a set of participants $V$, most of which obey the protocol, but a constant fraction may be Byzantine, i.e. behave arbitrarily, e.g. provide false or inconsistent information or randomly go offline when they ought to be online. +We need to incorporate into the definition of Byzantine agreement that we have access to a protocol that would achieve eventual consensus if we did not affect it. Consider a typical definition of a multi-values Byzantine agreement: +We have a set of participants $V$, the majority of whom obey the protocol, but a constant fraction may be Byzantine, meaning they behave arbitrarily, e.g. provide false or inconsistent information or randomly go offline when they ought to be online. \begin{definition} A protocol for multi-valued Byzantine agreement has a set of values $S$, a set of voters $V$, a constant fraction of which may be Byzantine, each of whom start with an initial value $s_v \in S$ for each $v \in V$ and in the end each voter decides a final value $f_v \in S$ such that the following holds: