--- a/ChengsongTanPhdThesis/Chapters/Introduction.tex	Tue Jun 14 18:06:33 2022 +0100
+++ b/ChengsongTanPhdThesis/Chapters/Introduction.tex	Thu Jun 23 16:09:40 2022 +0100
@@ -19,7 +19,7 @@
 %\newcommand{\sflataux}[1]{\textit{sflat}\_\textit{aux} \, #1}
 \newcommand\sflat[1]{\llparenthesis #1 \rrparenthesis }
 \newcommand{\ASEQ}[3]{\textit{ASEQ}_{#1} \, #2 \, #3}
-\newcommand{\bderssimp}[2]{#1 \backslash_{bsimp} #2}
+\newcommand{\bderssimp}[2]{#1 \backslash_{bsimps} #2}
 \newcommand{\rderssimp}[2]{#1 \backslash_{rsimp} #2}
 \newcommand{\bders}[2]{#1 \backslash #2}
 \newcommand{\bsimp}[1]{\textit{bsimp}(#1)}
@@ -30,7 +30,7 @@
 \newcommand{\ZERO}{\mbox{\bf 0}}
 \newcommand{\ONE}{\mbox{\bf 1}}
 \newcommand{\AALTS}[2]{\oplus {\scriptstyle #1}\, #2}
-\newcommand{\rdistinct}[2]{\textit{distinct} \; \textit{#1} \; #2}
+\newcommand{\rdistinct}[2]{\textit{rdistinct} \; \textit{#1} \; #2}
 \newcommand\hflat[1]{\llparenthesis  #1 \rrparenthesis_*}
 \newcommand\hflataux[1]{\llparenthesis #1 \rrparenthesis_*'}
 \newcommand\createdByStar[1]{\textit{createdByStar}(#1)}
@@ -38,6 +38,7 @@
 \newcommand\myequiv{\mathrel{\stackrel{\makebox[0pt]{\mbox{\normalfont\tiny equiv}}}{=}}}
 
 \def\bnullable{\textit{bnullable}}
+\def\bnullables{\textit{bnullables}}
 \def\Some{\textit{Some}}
 \def\None{\textit{None}}
 \def\code{\textit{code}}
@@ -60,6 +61,7 @@
 \def\DFA{\textit{DFA}}
 \def\NFA{\textit{NFA}}
 \def\bmkeps{\textit{bmkeps}}
+\def\bmkepss{\textit{bmkepss}}
 \def\retrieve{\textit{retrieve}}
 \def\blexer{\textit{blexer}}
 \def\flex{\textit{flex}}
@@ -81,7 +83,7 @@
 \def\lf{\textit{lf}}
 \def\PD{\textit{PD}}
 \def\suffix{\textit{Suffix}}
-
+\def\distinctBy{\textit{distinctBy}}
 
 \def\size{\mathit{size}}
 \def\rexp{\mathbf{rexp}}
@@ -97,9 +99,15 @@
 \newcommand\rnullable[1]{\textit{rnullable}(#1)}
 \newcommand\rsize[1]{\llbracket #1 \rrbracket_r}
 \newcommand\asize[1]{\llbracket #1 \rrbracket}
-\newcommand\rerase[1]{ (#1)\downarrow_r}
+\newcommand\rerase[1]{ (#1)_{\downarrow_r}}
+
 \newcommand\ChristianComment[1]{\textcolor{blue}{#1}\\}
 
+
+\def\rflts{\textit{rflts}}
+\def\rrewrite{\textit{rrewrite}}
+\def\bsimpalts{\textit{bsimp}_{ALTS}}
+
 \def\erase{\textit{erase}}
 \def\STAR{\textit{STAR}}
 \def\flts{\textit{flts}}
@@ -330,7 +338,7 @@
 But there are problems with current practical implementations.
 First thing is that the running time might blow up.
 The second problem is that they might be error-prone on certain
-cases that are very easily spotted by a human.
+very simple cases.
 In the next part of the chapter, we will look into reasons why 
 certain regex engines are running horribly slow on the "catastrophic"
 cases and propose a solution that addresses both of these problems