
diff -r 638663141103 -r 9c4b9bda974c slides/slides02.tex
--- a/slides/slides02.tex	Sun Sep 30 12:01:14 2018 +0100
+++ b/slides/slides02.tex	Sun Sep 30 23:38:38 2018 +0100
@@ -44,14 +44,14 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{\begin{tabular}{@ {}c@ {}}
-    An Efficient Regular\\[-1mm] 
-    Expression Matcher\end{tabular}}
+\begin{frame}[t]
+  \frametitle{\Large
+    Lets Implement an Efficient\\[-2mm] 
+    Regular Expression Matcher}
 
 \footnotesize
 \begin{center}
-  {\normalsize Graphs: \bl{$a^{?\{n\}} \cdot a^{\{n\}}$} and strings \bl{$\underbrace{\,a\ldots a\,}_{n}$}}\smallskip\\
+  {\normalsize Graphs: \bl{$a^{?\{n\}} \cdot a^{\{n\}}$} and strings \bl{$\underbrace{\,a\ldots a\,}_{n}$}}\medskip\\
 \begin{tabular}{@{}cc@{}}
 \begin{tikzpicture}
 \begin{axis}[
@@ -90,7 +90,7 @@
     width=5cm,
     height=4.5cm,
     legend entries={Scala V2,Scala V3},
-    legend pos=north west,
+    legend pos=north east,
     legend cell align=left]
 \addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
 \addplot[black,mark=square*,mark options={fill=white}] table {re3.data};
@@ -100,7 +100,7 @@
 \end{center}
 
 \small
-In the handouts is a similar graph for \bl{$(a^*)^* \cdot b$} and Java.
+In the handouts is a similar graph for \bl{$(a^*)^* \cdot b$} and Java 8.
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
@@ -113,11 +113,11 @@
 \item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\bigskip
 \item Evil regular expressions\medskip
 \begin{itemize}
-\item \bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}
+\item \bl{$a^{?\{n\}} \cdot a^{\{n\}}$}
 \item \bl{$(a^*)^*$}
 \item \bl{$([a$\,-\,$z]^+)^*$}
 \item \bl{$(a + a \cdot a)^*$}
-\item \bl{$(a + a?)^*$}
+\item \bl{$(a + a^?)^*$}
 \end{itemize}
 
 \item sometimes also called \alert{catastrophic backtracking}
@@ -231,6 +231,8 @@
 \bl{A^0 \cup A^1 \cup A^2 \cup A^3 \cup A^4 \cup \ldots}
 \]
 
+or
+
 \small
 \[
 \bl{\{[]\} \;\cup\; A \;\cup\; A\,@\,A \;\cup\; 
@@ -244,8 +246,9 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] 
-  Regular Expression\end{tabular}}
+\frametitle{
+    The Meaning of a\\[-2mm] 
+    Regular Expression}
 
 \begin{textblock}{15}(1,4)
  \begin{tabular}{rcl}
@@ -268,17 +271,19 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Semantic Derivative}
+\begin{frame}[t]
+\frametitle{Semantic Derivative\\[5mm]}
+
+  
 
 \begin{itemize}
 \item The \alert{\bf Semantic Derivative} of a 
-\underline{language}\\ wrt to a character \bl{$c$}:
+\underline{language}\\ w.r.t.~to a character \bl{$c$}:
 \bigskip
 
 \begin{center}
 \bl{$\Der\,c\,A \dn \{ s \;|\;  c\!::\!s \in A\}$ } 
-\end{center}\bigskip\bigskip\bigskip
+\end{center}\bigskip
 
 For \bl{$A = \{\textit{foo}, \textit{bar}, \textit{frak}\}$} then
 
@@ -286,7 +291,7 @@
 \bl{\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l}
 $\Der\,f\,A$ & $=$ & $\{\textit{oo}, \textit{rak}\}$\\
 $\Der\,b\,A$ & $=$ &  $\{\textit{ar}\}$\\  
-$\Der\,a\,A$ & $=$ & $\{\}$\\\pause
+$\Der\,a\,A$ & $=$ & $\{\}$\pause
 \end{tabular}}
 \end{center}
 
@@ -304,7 +309,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}The Specification\\ of Matching\end{tabular}}
+\frametitle{The Specification\\ for Matching}
 
 \begin{bubble}[10cm]
 \large
@@ -354,9 +359,10 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}
+\frametitle{
  When Are Two Regular\\[-1mm]
- Expressions Equivalent?\end{tabular}}
+ Expressions Equivalent?}
+
 \large
 \begin{center}
 \bl{$r_1 \equiv r_2 \;\;\dn\;\; L(r_1) = L(r_2)$}
@@ -404,7 +410,7 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{Simplification Rules}
-
+ 
 \begin{center}
 \bl{\begin{tabular}{rcl}
 $r + \ZERO$  & $\equiv$ & $r$\\
@@ -423,7 +429,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{A Matching Algorithm}
+\frametitle{A Matching Algorithm (1)}
 
 
 \ldots{}whether a regular expression can match the empty string:
@@ -497,11 +503,11 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{The Algorithm}
+\frametitle{\mbox{The Brzozowski Algorithm}}
 
 \begin{center}
 \begin{tabular}{l} 
-\bl{$\textit{matches}\,r\,s \dn \textit{nullable}(\ders\,r\,s)$}  
+\bl{$\textit{matches}\,r\,s \dn \textit{nullable}(\ders\;s\;r)$}  
 \end{tabular}
 \end{center}
 
@@ -511,7 +517,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{An Example}
+\frametitle{Brzozowski: An Example}
 
 Does \bl{$r_1$} match \bl{$abc$}?
 \begin{center}
@@ -521,7 +527,7 @@
 Step 3: & build derivative of \bl{$c$} and \bl{$r_3$} & \bl{$(r_4 = \der\,c\,r_3)$}\smallskip\\
 Step 4: & the string is exhausted: & \bl{($nullable(r_4))$}\\
         & test whether \bl{$r_4$} can recognise\\
-        & the empty string\smallskip\\
+        & the empty string\medskip\\
 Output: & result of the test\\
         & $\Rightarrow \bl{\textit{true}} \,\text{or}\, 
                        \bl{\textit{false}}$\\        
@@ -554,7 +560,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Oops\ldots\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{Oops\ldots \;\bl{$a^{?\{n\}} \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -588,8 +594,8 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{A Problem}
+\begin{frame}[t]
+\frametitle{A Problem\medskip}
 
 We represented the ``n-times'' \bl{$a^{\{n\}}$} as a 
 sequence regular expression:
@@ -634,7 +640,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{Brzozowski: \bl{$a^{?\{n\}} \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -687,7 +693,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{Simplifiaction}
+\frametitle{Simplification Rules}
 
 \begin{center}
 \bl{\begin{tabular}{rcl}
@@ -702,7 +708,7 @@
 \end{center}
 
 \footnotesize
-\lstinputlisting{../progs/app60.scala}
+\lstinputlisting[firstline=22,lastline=26]{../progs/app6.scala}
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
@@ -710,7 +716,7 @@
 \begin{frame}[c]
 
 \footnotesize
-\lstinputlisting{../progs/app6.scala}
+\lstinputlisting[firstline=1,lastline=21]{../progs/app6.scala}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
@@ -718,7 +724,7 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{\bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}}
+\frametitle{Brzozowski: \bl{$a^{?\{n\}} \cdot a^{\{n\}}$}}
 
 \begin{center}
 \begin{tikzpicture}
@@ -747,41 +753,81 @@
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\begin{frame}[c]
-%\frametitle{\bl{$(a^*)^* \cdot b$}}
-%
-%\begin{center}
-%\begin{tikzpicture}
-%  \begin{axis}[
-%    xlabel={$n$},
-%    x label style={at={(1.09,0.0)}},
-%    ylabel={time in secs},
-%    enlargelimits=false,
-%    xmax=27,
-%    xtick={0,5,...,20},
-%    ytick={0,5,...,25},
-%    ymax=13,
-%    scaled ticks=false,
-%    axis lines=left,
-%    width=9cm,
-%    height=5cm, 
-%    legend entries={Scala V2},
-%    legend pos=north west,
-%    legend cell align=left]
-%\addplot[green,mark=square*,mark options={fill=white}] table {re2a.data};
-%% still needs to be done
-%%\addplot[black,mark=square*,mark options={fill=white}] table {re3a.data};
-%\end{axis}
-%\end{tikzpicture}
-%\end{center}
-%
-%\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
-\frametitle{\bl{$(a^*)^* \cdot b$}}
+  \frametitle{
+    Another Example\\[-1mm]
+    in Java \liningnums{8} and Python}
+
+\begin{center}
+\begin{tikzpicture}
+  \begin{axis}[
+    xlabel={$n$},
+    x label style={at={(1.05,0.0)}},
+    ylabel={time in secs},
+    enlargelimits=false,
+    xtick={0,5,...,30},
+    xmax=33,
+    ymax=35,
+    ytick={0,10,...,30},
+    scaled ticks=false,
+    axis lines=left,
+    width=9cm,
+    height=5cm, 
+    legend entries={Java 8, Python},  
+    legend pos=north west,
+    legend cell align=left]
+\addplot[blue,mark=*, mark options={fill=white}] table {re-python2.data};
+\addplot[cyan,mark=*, mark options={fill=white}] table {re-java.data};
+\end{axis}
+\end{tikzpicture}
+\end{center}
+
+Regex: \bl{$(a^*)^* \cdot b$}
+
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{Same Example in Java \liningnums{9}+}
+
+\begin{center}
+\begin{tikzpicture}
+  \begin{axis}[
+    xlabel={$n$},
+    x label style={at={(1.09,-0.15)}},
+    ylabel={time in secs},
+    scaled x ticks=false,
+    enlargelimits=false,
+    xtick distance=10000,
+    xmax=44000, 
+    ytick={0,10,...,30}, 
+    ymax=35, 
+    axis lines=left,
+    width=9cm,
+    height=5cm, 
+    legend entries={Java \liningnums{9}+},
+    legend pos=north west,
+    legend cell align=left]
+\addplot[blue,mark=square*,mark options={fill=white}] table {re-java9.data};
+\end{axis}
+\end{tikzpicture}
+\end{center}
+
+Regex: \bl{$(a^*)^* \cdot b$}
+
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
+
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{and with Brzozowski}
 
 \begin{center}
 \begin{tikzpicture}
@@ -789,14 +835,17 @@
     xlabel={$n$},
     x label style={at={(1.09,0.0)}},
     ylabel={time in secs},
+    scaled x ticks=false,
+    xtick distance=2000000,
     enlargelimits=false,
+    xmax=6400000, 
     ytick={0,10,...,30},
     ymax=35,
     axis lines=left,
     width=9cm,
     height=5cm, 
     legend entries={Scala V3},
-    legend pos=north east,
+    legend pos=north west,
     legend cell align=left]
 %\addplot[green,mark=square*,mark options={fill=white}] table {re2a.data};
 \addplot[black,mark=square*,mark options={fill=white}] table {re3a.data};
@@ -804,11 +853,13 @@
 \end{tikzpicture}
 \end{center}
 
+Regex: \bl{$(a^*)^* \cdot b$}
+
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
+
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
 \frametitle{What is good about this Alg.}




