
diff -r 788f4aa28bc5 -r 1260b383ae2c etnms/etnms.tex
--- a/etnms/etnms.tex	Sat Feb 08 21:34:50 2020 +0000
+++ b/etnms/etnms.tex	Sat Feb 08 21:37:05 2020 +0000
@@ -107,6 +107,25 @@
   negation and back-references.
 \end{abstract}
 
+
+\section{Introduction}
+
+While we believe derivatives of regular expressions, written
+$r\backslash s$, are a beautiful concept (in terms of ease of
+implementing them in functional programming languages and in terms of
+reasoning about them formally), they have one major drawback: every
+derivative step can make regular expressions grow drastically in
+size. This in turn has negative effect on the runtime of the
+corresponding lexing algorithms. Consider for example the regular
+expression $(a+aa)^*$ and the short string $aaaaaaaaaaaa$. The
+corresponding derivative contains already 8668 nodes where we assume
+the derivative is given as a tree. The reason for the poor runtime of
+the derivative-based lexing algorithms is that they need to traverse
+such trees over and over again. The solution is to find a complete set
+of simplification rules that keep the sizes of derivatives uniformly
+small.
+
+
 \section{Recapitulation of Concepts From the Last Report}
 
 \subsection*{Regular Expressions and Derivatives}
@@ -735,23 +754,7 @@
 
 
 
-\section{Introduction}
-
-While we believe derivatives of regular expressions, written
-$r\backslash s$, are a beautiful concept (in terms of ease of
-implementing them in functional programming languages and in terms of
-reasoning about them formally), they have one major drawback: every
-derivative step can make regular expressions grow drastically in
-size. This in turn has negative effect on the runtime of the
-corresponding lexing algorithms. Consider for example the regular
-expression $(a+aa)^*$ and the short string $aaaaaaaaaaaa$. The
-corresponding derivative contains already 8668 nodes where we assume
-the derivative is given as a tree. The reason for the poor runtime of
-the derivative-based lexing algorithms is that they need to traverse
-such trees over and over again. The solution is to find a complete set
-of simplification rules that keep the sizes of derivatives uniformly
-small.
-
+\section{Current Work and Progress}
 For reasons beyond this report, it turns out that a complete set of
 simplification rules depends on values being encoded as
 bitsequences.\footnote{Values are the results the lexing algorithms




