From 2f9e6db4b5fddeb1eebea58acdfcbd921fe74fb5 Mon Sep 17 00:00:00 2001
From: GoodDaisy <90915921+GoodDaisy@users.noreply.github.com>
Date: Tue, 24 Oct 2023 17:12:45 +0800
Subject: [PATCH] fix minor typos

---
 NPoS/npos.py | 2 +-
 pdf/disc.tex | 4 ++--
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/NPoS/npos.py b/NPoS/npos.py
index eec386a..c09bf0f 100644
--- a/NPoS/npos.py
+++ b/NPoS/npos.py
@@ -264,7 +264,7 @@ def setuplists(votelist):
     flat list of nominators and the latter is a flat list of validator candidates.
 
     Instead of Python's dict here, you can use anything with O(log n) addition and lookup. We can
-    also use a hashmap like dict, by generating a random constant r and useing H(canid+r) since the
+    also use a hashmap like dict, by generating a random constant r and using H(canid+r) since the
     naive thing is obviously attackable.
     '''
     nomlist = [nominator(votetuple[0], votetuple[1], votetuple[2]) for votetuple in votelist]
diff --git a/pdf/disc.tex b/pdf/disc.tex
index 8e8a094..5287d0b 100644
--- a/pdf/disc.tex
+++ b/pdf/disc.tex
@@ -46,7 +46,7 @@
 
 \category{} %optional, e.g. invited paper
 
-\relatedversion{} %optional, e.g. full version hosted on arXiv, HAL, or other respository/website
+\relatedversion{} %optional, e.g. full version hosted on arXiv, HAL, or other repository/website
 %\relatedversion{A full version of the paper is available at \url{...}.}
 
 \supplement{}%optional, e.g. related research data, source code, ... hosted on a repository like zenodo, figshare, GitHub, ...
@@ -808,7 +808,7 @@ Then any participant sees that if there is an $n$ such that
 \item[(ii)] the indicators the last finalized block height of blocks $n-100$ to $n$ in their best chain have median at most $n-1050$ and
 \item[(iii]) $n$ is the minimum that satisifies (i) and (ii)
 \end{itemize}
-then they switch to the best voter set given by block $n$. If the same block at height $n$ is on everyone's best chain, which can be shown to occur with high probability given (i) for many block production mechanisms, then everyone will eventually agree that we should switch to the voter set given by that block. If any $100$ consectutive blocks of the best chain are produced by honest and synchronised block producers then this will only happen if GRANDPA fails to finalize any block in the time it took to produce $1000$ blocks.
+then they switch to the best voter set given by block $n$. If the same block at height $n$ is on everyone's best chain, which can be shown to occur with high probability given (i) for many block production mechanisms, then everyone will eventually agree that we should switch to the voter set given by that block. If any $100$ consecutive blocks of the best chain are produced by honest and synchronised block producers then this will only happen if GRANDPA fails to finalize any block in the time it took to produce $1000$ blocks.
 
 \subsection{Alternatives to the last block hash}