From 350d4fb6f6368aa083d0670f712e538ced126e3c Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Thu, 14 Oct 2021 16:45:53 +0200
Subject: Adjust words

---
 mgr.tex | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

(limited to 'mgr.tex')

diff --git a/mgr.tex b/mgr.tex
index 9aa3d92..5ccc072 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -277,7 +277,7 @@ automata.
 \subsection{Monadic Second Order (MSO) Logic}
 % def of MSO
 
-From a logical point of view, the trees we work with can be seen as structures
+From a logic point of view, the trees we work with can be seen as structures
 over a signature with a single binary relation $E$ and unary relations $U_a$ for
 each $a \in \Sigma$. $E(v, w)$ represents a (directed from parent to child) edge
 from $v$ to $w$. $U_a(v)$ signifies that $v$'s label is $a$.
@@ -581,12 +581,12 @@ Items \ref{obs-descendants} and \ref{obs-ancestors} together give us item
 \ref{obs-conclusion}.
 
 In our problem, we only care about ancestors of $y$ that are marked. So
-we perform one final modification of our data structure: for all non-black
+we perform one final modification of our data structure: for all non-marked
 vertices $v$, we change $\prefixtable[\indextable[v]]$ to $\infty$ (which can be
 represented by $n+1$, an integer greater than any node's pre-order label). With
 \prefixtable\ modified like this, we observe that now the minimum value of
 $\prefixtable[\indextable[y], \indextable[x] - 1]$ corresponds exactly to the
-answer of our queries -- the highest black node between $x$ and $y$.
+answer of our queries -- the highest marked node between $x$ and $y$.
 
 We preprocess \prefixtable\ for RMQ queries in linear time.
 
-- 
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