From ccf7910c74c8c09affd5e7d5102e69ebee719524 Mon Sep 17 00:00:00 2001 From: Jeff Burdges Date: Wed, 7 Nov 2018 14:46:28 +0100 Subject: [PATCH] Run on sentence was kinda ambiguious. Added ??? for unspecified oracle property --- pdf/grandpa.tex | 5 ++--- 1 file changed, 2 insertions(+), 3 deletions(-) diff --git a/pdf/grandpa.tex b/pdf/grandpa.tex index ce06599..518ead1 100644 --- a/pdf/grandpa.tex +++ b/pdf/grandpa.tex @@ -45,7 +45,7 @@ We present a finality gadget that works in a partially synchronous network model 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: +\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 voter $v \in V$ starts with an initial value $s_v \in S$ and, in the end, decides a final value $f_v \in S$ such that the following holds: \begin{itemize} \item {\bf Agreement}: All honest voters decide the same value for $f_v$ @@ -57,8 +57,7 @@ We have a set of participants $V$, the majority of whom obey the protocol, but a We can change this definition to assume that instead of having an initial value, all voters have access to an external protocol, an oracle for values, that achieves eventual consensus in that it returns the same value to all voters when called after some time. -\begin{definition} A protocol for multi-valued Byzantine finality gadget problem has a set of values $S$, a set of voters $V$, a constant fraction of which may be Byzantine, each of whom has access to an oracle $A$ with the property that in the end each voter decides a final value $f_v \in S$ such that the following holds: - +\begin{definition} A protocol for multi-valued Byzantine finality gadget problem has a set of values $S$, a set of voters $V$, a constant fraction of which may be Byzantine. Each voter $v \in V$ has access to an oracle $A$ with the property that ??? in the end each voter decides a final value $f_v \in S$ such that the following holds: \begin{itemize} \item {\bf Agreement:} All honest voters decide the same value for $f_v$