From 2d01c6fea258521be69f66c7b96b2fd78133ed18 Mon Sep 17 00:00:00 2001
From: krakenlake <119040831+krakenlake@users.noreply.github.com>
Date: Thu, 11 Apr 2024 11:35:59 +0200
Subject: [PATCH] Update statements-moonmath.tex

fixed 2 typos
---
 chapters/statements-moonmath.tex | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/chapters/statements-moonmath.tex b/chapters/statements-moonmath.tex
index 443578a5..34d23ac0 100644
--- a/chapters/statements-moonmath.tex
+++ b/chapters/statements-moonmath.tex
@@ -293,9 +293,9 @@ \subsection{Rank-1 Quadratic Constraint Systems}
 \label{sec:R1CS}
 Although decision functions are expressible in various ways, many contemporary proving systems require the decision function to be expressed in terms of a system of quadratic equations over a finite field. This is true in particular for pairing-based proving systems like the ones we describe in \chaptname{}  \ref{chapter:zk-protocols}, because in these cases it is possible to separate instance and witness and then check solutions to those equations ``in the exponent'' of pairing-friendly cryptographic groups.
 
-In this section, we will have a closer look at a particular type of quadratic equations called \term{Rank-1 (quadratic) Constraint Systems} (R1CS), which are a common standard in zero-knowledge proof systems (cf. appendix E of \cite{sasson-2013}). We will start with a general introduction to those constrain systems and then look at their relation to formal languages. Then we will look into a common way to compute solutions to those systems. 
+In this section, we will have a closer look at a particular type of quadratic equations called \term{Rank-1 (quadratic) Constraint Systems} (R1CS), which are a common standard in zero-knowledge proof systems (cf. appendix E of \cite{sasson-2013}). We will start with a general introduction to those constraint systems and then look at their relation to formal languages. Then we will look into a common way to compute solutions to those systems. 
 
-\subsubsection{R1CS representation} To understand what \term{Rank-1 (quadratic) Constraint Systems} )(R1CS) are in detail, let $\F$ be a field, $n$, $m$ and $k\in\N$ three numbers and $a_j^i$, $b_j^i$ and $c_j^i\in\F$ constants from $\F$ for every index $0\leq j \leq n+m$ and $1\leq i \leq k$. Then a \concept{rank-1 constraint system} is defined as the following set of $k$ many equations:\tbdsm{font size too small} 
+\subsubsection{R1CS representation} To understand what \term{Rank-1 (quadratic) Constraint Systems}) (R1CS) are in detail, let $\F$ be a field, $n$, $m$ and $k\in\N$ three numbers and $a_j^i$, $b_j^i$ and $c_j^i\in\F$ constants from $\F$ for every index $0\leq j \leq n+m$ and $1\leq i \leq k$. Then a \concept{rank-1 constraint system} is defined as the following set of $k$ many equations:\tbdsm{font size too small} 
 
 \begin{definition}[\deftitle{Rank-1 (quadratic) Constraint System}]\label{R1CS}
 \begin{equation}\label{eq:R1CS}