From 840dfd0f4eee7fd1f7f9b0035de72b9ec2d29a89 Mon Sep 17 00:00:00 2001
From: Marcin Chrzanowski <mc370754@students.mimuw.edu.pl>
Date: Fri, 5 Nov 2021 11:59:19 +0100
Subject: Reword and change font

---
 mgr.tex | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

(limited to 'mgr.tex')

diff --git a/mgr.tex b/mgr.tex
index 215540a..d3aa05c 100644
--- a/mgr.tex
+++ b/mgr.tex
@@ -307,16 +307,16 @@ MSO to automata direction in this work.
 \section{Query answering problems}\label{query-answering-problems}
 
 Consider a computational problem whose inputs are of the form $(S, q) \in
-\mathcal{S} \times Q$ for some set of \definedterm{structures} $\mathcal{S}$ and
-some set of \definedterm{queries} $Q$. This induces a \definedterm{query
-answering problem} which is divided into two phases:
+\mathcal{S} \times \mathcal{Q}$ for some set of \definedterm{structures}
+$\mathcal{S}$ and some set of \definedterm{queries} $\mathcal{Q}$. This induces
+a \definedterm{query answering problem} which is divided into two phases:
 
 \begin{description}
     \item[preprocessing] An input structure $S \in \mathcal{S}$ is given and a
-        \definedterm{preprocessing algorithm} outputs an indexing structure
+        \definedterm{preprocessing algorithm} outputs a data structure
         $S'$.
-    \item[queries] On-line queries $q_1, \ldots$ from $Q$ about $S$ need to be
-        handled, with access to the preprocessing output $S'$.
+    \item[queries] $S'$ is used to handle queries $q_1, \ldots$ from
+        $\mathcal{Q}$.
 \end{description}
 
 We are interested in the time complexities of both phases. We use the following
-- 
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