From 33bc7e620276f4269ee5f1820e5477135e020b3f Mon Sep 17 00:00:00 2001
From: Douglas Rumbaugh <dbr4@psu.edu>
Date: Sun, 8 Jun 2025 15:04:00 -0400
Subject: Julia updates v2

---
 chapters/introduction.tex | 28 +++++++++++++++-------------
 1 file changed, 15 insertions(+), 13 deletions(-)

(limited to 'chapters/introduction.tex')

diff --git a/chapters/introduction.tex b/chapters/introduction.tex
index 050a58b..6b6904a 100644
--- a/chapters/introduction.tex
+++ b/chapters/introduction.tex
@@ -1,7 +1,7 @@
 \chapter{Introduction}
 \label{chap:intro}
 
-\section{Motiviation}
+\section{Motivation}
 
 Modern relational database management systems (RDBMS) are founded
 upon a set-based representation of data~\cite{codd70}. This model is
@@ -39,17 +39,19 @@ data structures, which often already exist, are at the heart of such
 systems, meaningfully using such a data structure in a database requires
 adding a large number of additional features. 
 
-To be useful within the context of a database, a data structure must
+A recent work on extending Datalog with support for user-defined data
+structures demonstrates both the benefits and challenges associated
+with the use of specialized indices. It showed showed significant
+improvements in query processing time and space requirements when
+using custom indices, but required that the user-defined structures
+have support for concurrent updates~\cite{byods-datalog}. In practice,
+to be useful within the context of a database, a data structure must
 support inserts and deletes (collectively referred to as updates),
 as well as concurrency support that satisfies standardized isolation
 semantics~\cite{cowbook}, support for crash recovery of the index in the
-case of a system failure~\cite{aries}, and possibly more. As an example,
-a recent work on extended Datalog with support for user-defined data
-structures showed significant improvements in query processing time and
-space requirements, but required that the user-defined structures have
-support for concurrent updates~\cite{byods-datalog}.  The process of
-adding these features to data structures that currently lack them is
-not straightfoward and can take an extensive amount of time and effort.
+case of a system failure~\cite{aries}, and possibly more. The process
+of extending an existing or novel data structure with support for all
+of these functions is a major barrier to their use.
 
 As a current example that demonstrates this problem, consider the recent
 development of learned indices. These are a broad class of data structure
@@ -91,7 +93,7 @@ step in this direction.
 
 \section{Existing Attempts}
 
-At present, there are several lines of work targetted at reducing
+At present, there are several lines of work targeted at reducing
 the development burden associated with creating specialized indices. We
 classify them into three broad categories,
 
@@ -134,7 +136,7 @@ to maximize the overall performance of the workload. Although some work
 in this area suggests generalization to more complex data types, such
 as multi-dimensional data~\cite{fluid-ds}, this line is broadly focused
 on creating instance-optimal indices for workloads that databases are
-already well equiped to handle. While this task is quite important, it
+already well equipped to handle. While this task is quite important, it
 is not precisely the work that we are trying to accomplish here. And,
 because the techniques are limited to specified sets of structural
 primitives, it isn't clear that the approach can be usefully extended
@@ -163,7 +165,7 @@ difficulties of index development.
 
 The final approach is  automatic feature extension. More specifically,
 we will consider dynamization,\footnote{
-	This is alternative called a static-to-dynamic transformation,
+	This is alternatively called a static-to-dynamic transformation,
 	or dynamic extension, depending upon the source. These terms
 	all refer to the same process.
 } the automatic extension of an existing static data structure with
@@ -209,7 +211,7 @@ faced by most classical dynamization techniques.
 
 Specifically, the proposed work will address the following points,
 \begin{enumerate}
-    \item The proposal of a theoretical framework for analysing queries
+    \item The proposal of a theoretical framework for analyzing queries
           and data structures that extends existing theoretical
           approaches and allows for more data structures to be dynamized.
     \item The design of a system based upon this theoretical framework
-- 
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