From db0c092d285fe5140254e046fcd81aabd4de8f4a Mon Sep 17 00:00:00 2001
From: Yoichi Hirai <i@yoichihirai.com>
Date: Wed, 10 May 2017 16:16:41 +0200
Subject: [PATCH] Fix whitespaces

---
 Paper.tex | 9 +++++----
 1 file changed, 5 insertions(+), 4 deletions(-)

diff --git a/Paper.tex b/Paper.tex
index 61d26dda..5e8536f6 100644
--- a/Paper.tex
+++ b/Paper.tex
@@ -877,10 +877,10 @@ \subsection{Execution Overview}
 \end{eqnarray}
 \begin{equation} \label{eq:X-def}
 X\big( (\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \big) \equiv \begin{cases}
-\big(\varnothing, \boldsymbol{\mu}, A^0, I, \varnothing\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I)\\
+\big(\varnothing, \boldsymbol{\mu}, A^0, I, \varnothing\big) & \text{if} \quad Z(\boldsymbol{\sigma}, \boldsymbol{\mu}, I) \\
 \big(\varnothing, \boldsymbol{\mu}', A^0, I, \mathbf{o}\big) & \text{if} \quad w = \text{\small REVERT} \\
-O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \cdot \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing\\
-X\big(O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \text{otherwise}\\
+O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I) \cdot \mathbf{o} & \text{if} \quad \mathbf{o} \neq \varnothing \\
+X\big(O(\boldsymbol{\sigma}, \boldsymbol{\mu}, A, I)\big) & \text{otherwise} \\
 \end{cases}
 \end{equation}
 
@@ -2017,7 +2017,7 @@ \subsection{Instruction Set}
 &&&& $A' \equiv A \Cup A^+$ \\
 &&&& $t \equiv \boldsymbol{\mu}_\mathbf{s}[1] \mod 2^{160}$ \\
 &&&& where $x=0$ if the code execution for this operation failed due to an exceptional halting \\
-&&&& (or for a \text{\small REVERT}) $\boldsymbol{\sigma}' = \varnothing$ or if  \\
+&&&& (or for a \text{\small REVERT}) $\boldsymbol{\sigma}' = \varnothing$ or if \\
 &&&& $\boldsymbol{\mu}_\mathbf{s}[2] > \boldsymbol{\sigma}[I_a]_b$ (not enough funds) or $I_e = 1024$ (call depth limit reached); $x=1$ \\
 &&&& otherwise. \\
 &&&& $\boldsymbol{\mu}'_i \equiv M(M(\boldsymbol{\mu}_i, \boldsymbol{\mu}_\mathbf{s}[3], \boldsymbol{\mu}_\mathbf{s}[4]), \boldsymbol{\mu}_\mathbf{s}[5], \boldsymbol{\mu}_\mathbf{s}[6])$ \\
@@ -2077,6 +2077,7 @@ \subsection{Instruction Set}
 &&&& The last argument of $\Theta$ is $\bot$. \\
 0xfd & {\small REVERT} & 2 & 0 & Halt execution reverting state changes
                  but returning data and gas. \\
+0xfd & {\small REVERT} & 2 & 0 & Halt execution reverting state changes but returning data and gas. \\
 &&&& The effect of this operation is described in (\ref{eq:X-def}). \\
 &&&& For the gas calculation, we need to define the memory usage: \\
 &&&& $\boldsymbol{\mu}'_i \equiv M(\boldsymbol{\mu}_i, \boldsymbol{\mu}_\mathbf{s}[0], \boldsymbol{\mu}_\mathbf{s}[1])$ \\