
diff -r cd0ceaf89c1d -r c51178fa85fe slides01.tex
--- a/slides01.tex	Sun May 05 22:02:29 2019 +0100
+++ b/slides01.tex	Wed May 08 22:09:59 2019 +0100
@@ -3,7 +3,7 @@
 \usepackage{./graph}
 \usepackage{./langs}
 \usepackage{./data}
-
+\usepackage{changepage}
 \hfuzz=220pt 
 
 \lstset{language=Scala,
@@ -82,7 +82,78 @@
 60000 43.0327746
 \end{filecontents}
 
+\begin{filecontents}{re-usize.data}
+1  16
+2  33
+3  63
+4  108
+5  181
+6  297
+7  484
+8  785
+9  1271
+10  2056
+11  3325
+12  5377
+13  8696
+14  14065
+15  22751
+16  36804
+17  59541
+18  96329
+19  155852
+20  252161
+21  407991
+22  660128
+23  1068093
+24  1728193
+25  2796256
+26  4524417
+27  7320639
+\end{filecontents}
 
+\begin{filecontents}{re-ssize.data}
+1  12
+2  19
+3  19
+4  19
+5  19
+6  19
+7  19
+8  19
+9  19
+10  19
+11  19
+12  19
+13  19
+14  19
+15  19
+16  19
+17  19
+18  19
+19  19
+20  19
+21  19
+22  19
+23  19
+24  19
+25  19
+26  19
+27  19
+28  19
+29  19
+30  19
+31  19
+32  19
+33  19
+34  19
+35  19
+36  19
+37  19
+38  19
+39  19
+40  19
+\end{filecontents}
 
 \begin{document}
 
@@ -96,9 +167,9 @@
 \begin{frame}[t]
 \frametitle{%  
   \begin{tabular}{@ {}c@ {}}
-  \\[-3mm]
-  \LARGE Compilers and \\[-1mm] 
-  \LARGE Formal Languages (1)\\[-3mm] 
+  \\[-1mm]
+  \LARGE Fast Regular Expression  \\[-1mm] 
+  \LARGE Matching Using Derivatives\\[-3mm] 
   \end{tabular}}
 
   \begin{center}
@@ -110,18 +181,46 @@
   \normalsize
   \begin{center}
   \begin{tabular}{ll}
-  Email:  & christian.urban at kcl.ac.uk\\
-  Office: & N\liningnums{7.07} (North Wing, Bush House)\\
-  Slides: & KEATS
+  %Email:  & christian.urban at kcl.ac.uk\\
+  %Office: & N\liningnums{7.07} (North Wing, Bush House)\\
+  %Slides: & KEATS
+  Student: & Chengsong Tan\\
+  Supervisor: & Christian Urban \\
+  Date: & 2019/5/10
   \end{tabular}
   \end{center}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{Why Study Compilers?}
+\frametitle{Regular Expressions}
+
+Their inductive definition:\\
+\hspace{10pt}
+\vspace{100pt}
+
+\begin{textblock}{6}(1.5,3.5)
+  \begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
+  \bl{$r$} & \bl{$::=$}  & \bl{$\ZERO$}  & nothing\\
+         & \bl{$\mid$} & \bl{$\ONE$}       & empty string / \pcode{""} / $[]$\\
+         & \bl{$\mid$} & \bl{$c$}                         & character\\
+         & \bl{$\mid$} & \bl{$r_1 + r_2$}  & alternative / choice\\
+         & \bl{$\mid$} & \bl{$r_1 \cdot r_2$} & sequence\\
+         & \bl{$\mid$} & \bl{$r^*$}            & star (zero or more)\\
+  \end{tabular}
+  \end{textblock}
+  
+ \begin{itemize}
+\item { Formalized by Stephen Coles Kleene in 1950s} 
+\item {\bf What could be possibly interesting?} 
+ \end{itemize} 
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\iffalse
+\begin{frame}[t]
+\frametitle{Regular Expressions}
 
 John Regehr {\small(Univ.~Utah, LLVM compiler hacker)}\smallskip\\
 
@@ -162,9 +261,11 @@
 \end{itemize}}}
 
 \end{frame}
+\fi
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\iffalse
 \begin{frame}[c]
 \frametitle{Why Bother?}
 
@@ -257,15 +358,24 @@
 matching \texttt{[a?]\{n\}[a]\{n\}} and \texttt{(a*)*b}
 against $\underbrace{\texttt{a}...\texttt{a}}_n$
 \end{frame} 
+\fi
 
-\begin{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[c]
+\frametitle{Catastrophic Backtracking}
+
+\begin{columns}
 \begin{column}{.5\textwidth}
+
 \begin{tikzpicture}
 \begin{axis}[
     xlabel={$n$},
-    x label style={at={(1.05,0.0)}},
+    x label style={at={(1.07,0.0)}},
     ylabel={time in secs},
-    y label style={at={(0.06,0.5)}},
+    %y label style={at={(0.06,0.5)}},
     enlargelimits=false,
     xtick={0,5,...,30},
     xmax=33,
@@ -273,20 +383,21 @@
     ytick={0,10,...,40},
     scaled ticks=false,
     axis lines=left,
-    width=6cm,
-    height=4.5cm, 
+    width=5cm,
+    height=4cm, 
     legend entries={Python, Java 8},  
     legend pos=north west]
 \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}
+
 \begin{tikzpicture}
 \begin{axis}[
     xlabel={$n$},
-    x label style={at={(1.05,0.0)}},
+    x label style={at={(1.07,0.0)}},
     ylabel={time in secs},
-    y label style={at={(0.06,0.5)}},
+    %y label style={at={(0.06,0.5)}},
     %enlargelimits=false,
     %xtick={0,5000,...,30000},
     xmax=65000,
@@ -294,23 +405,58 @@
     ytick={0,10,...,40},
     scaled ticks=false,
     axis lines=left,
-    width=6cm,
-    height=4.5cm, 
+    width=5cm,
+    height=4cm, 
     legend entries={Java 9},  
     legend pos=north west]
 \addplot[cyan,mark=*, mark options={fill=white}] table {re-java9.data};
 \end{axis}
 \end{tikzpicture}
 \end{column}
+\end{columns}\bigskip
+\center
+matching  \texttt{(a*)*b}
+against $\underbrace{\texttt{a}...\texttt{a}}_n$
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[fragile]
+\frametitle{Impact}
+
+\begin{itemize}
+\item Network Traffic Analysis
+\begin{itemize}
+\item Snort:  > 5 million downloads
+\item Bro:  > 10000 downloads
+\item thousands of regexes
+\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\medskip
+
+\end{itemize}
+
+\begin{verbatim}
+ Jan 2 00:53:19 talisker sshd: Received disconnect from 110.53.183.227: [preauth]
+ Jan 2 00:58:31 talisker sshd: Received disconnect from 110.53.183.252: [preauth]
+ Jan 2 01:01:28 talisker sshd: Received disconnect from 221.194.47.236: [preauth]
+ Jan 2 01:03:59 talisker sshd: Received disconnect from 110.53.183.228: [preauth]
+ Jan 2 01:06:53 talisker sshd: Received disconnect from 221.194.47.245: [preauth]
+ ...
+\end{verbatim}
+
+
+\item Compilers: lexical analysis
+\end{itemize}
+
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[c]
 \frametitle{Evil Regular Expressions}
 
 \begin{itemize}
-\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\medskip
+%\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice (ReDoS)\medskip
 \item Evil regular expressions\medskip
 \begin{itemize}
 \item \bl{$(a^{?\{n\}}) \cdot a^{\{n\}}$}
@@ -318,584 +464,296 @@
 \item \bl{$([a$\,-\,$z]^+)^*$}
 \item \bl{$(a + a \cdot a)^*$}
 \item \bl{$(a + a^?)^*$}
+\item \bl{$\^(.*?,)\{11\}P$}
+\item \bl{$<html>.*?<head>.*?<title>.*?</title>.*?</head>.*?<body[^>]*>.*?</body>.*?</html>$}
+\end{itemize}
+
+\item Pearl Compatible Regular Expression(PCRE) \bl{$(r) \backslash 1$}
 \end{itemize}
 
-\item sometimes also called \alert{catastrophic backtracking}
-\item this is a problem for \alert{N}etwork \alert{I}ntrusion
-  \alert{D}etection systems, StackExchange, Atom editor
-\item \url{https://vimeo.com/112065252}  
+\end{frame}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[c]
+\frametitle{A Concrete Example}
+\begin{adjustwidth*}{}{-1.2cm} 
+\resizebox{13cm}{4cm}{
+
+    \begin{tikzpicture}[shorten >=1pt,node distance=2cm,on grid,auto] 
+    \node[state,initial] (q_0) {$0$};
+    \node[state] (q_1) [right = of q_0] {$1$};    
+    \node[state] (q_2) [right=of q_1] {$2$};
+    \node (q_dots1) [right = of q_2] {$\cdots$};
+    \node [state] (q_n) [right = of q_dots1] {$n$};
+    \node [state] (q_n1) [right = of q_n] {$n+1$};
+    \node[state] (q_n2) [right=of q_n1] {$n+2$};
+    \node[state,accepting] (q_n3) [right=of q_n2] {$n+3$};    
+
+    \path[->]
+    (q_0) edge [loop above] node {$*$} (q_0)
+    (q_0) edge node {$a$} (q_1)    
+    (q_1) edge node {$*$} (q_2)     
+    (q_2) edge node {$*$} (q_dots1)   
+    (q_dots1) edge node{$*$} (q_n)
+    (q_n) edge node{$*$} (q_n1)
+    (q_n1) edge node{$*$} (q_n2)
+    (q_n2) edge node{$*$} (q_n3);
+
+\draw [decorate,decoration={brace,amplitude=10pt,mirror,raise=10pt},yshift=0pt]
+(q_2.south west) -- (q_n1.south east) node [black,midway,yshift = -2cm] {\footnotesize n states};
+%\draw [decorate,decoration={brace,amplitude=10pt,mirror,raise=4pt},yshift=0pt]
+%(3.5,0.65) -- (3.5,6.5) node [black,midway,xshift=0.8cm] {\footnotesize
+%$P_2$};
+\end{tikzpicture}   
+}
+\end{adjustwidth*}
+
+\begin{itemize}
+\item
+NFA accepting Regex $.*a.{n}bc$
+\item
+Matching the string aaaaaaaaaaaaaaa.....abc
+\end{itemize}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[c]
+\frametitle{Brzozowski Derivative}
+
+\begin{itemize}
+\item Brzozowski invented in his 1964 Phd thesis
+\item Intuition: Chopping off the first character
+
+\begin{center}
+\bl{$A \backslash c \dn \{ s \;|\;  c\!::\!s \in A\}$ } 
+\end{center}
+\item
+For \bl{$A = \{\textit{foo}, \textit{bar}, \textit{frak}\}$} then
+
+\begin{center}
+\bl{\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}l}
+$A \backslash f $ & $=$ & $\{\textit{oo}, \textit{rak}\}$\\
+$A \backslash b $ & $=$ &  $\{\textit{ar}\}$\\  
+$A \backslash a $ & $=$ & $\{\}$\pause
+\end{tabular}}
+\end{center}
+\item
+\begin{tabular}{rp{4cm}}
+\bl {$r \,matches \,s=c_1c_2...c_n$}
+\bl{$\Leftrightarrow$}  \bl{$c_1c_2...c_n \in L(r)$}   \bl{$\Leftrightarrow$}\\
+  \bl{$c_2...c_n \in L(r) \backslash c_1$}\\
+\bl{$\Leftrightarrow$}  \bl{$\cdots$}\\
+\bl{$\Leftrightarrow$}  \bl{$[] \in ((L(r)\backslash c_1) \backslash c_2)\cdots\backslash c_n$}
+\end{tabular}
+
 \end{itemize}
 
 \end{frame}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\begin{frame}[c]
+\frametitle{Previous Example}
+
+\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=7cm,
+    height=3.5cm, 
+    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}
+
+\begin{center}
+\begin{tikzpicture}
+  \begin{axis}[
+    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=7cm,
+    height=3.5cm, 
+    legend entries={Simple Scala},
+    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};
+\end{axis}
+\end{tikzpicture}
+\end{center}
+
+Regex: \bl{$(a^*)^* \cdot b$} \space\space\space\space\space\space
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
+
+\end{frame}
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{The Goal of this Module}
+\begin{frame}[t]
+\frametitle{Optimization}
 
 \begin{center}
-  \begin{tikzpicture}[scale=1,
-                      node/.style={
-                      rectangle,rounded corners=3mm,
-                      very thick,draw=black!50,minimum height=18mm, minimum width=20mm,
-                      top color=white,bottom color=black!20}]
-
-  \node at (3.05, 1.8) {\Large\bf write a compiler};
-
-  \node (0) at (-2.3,0) {};  
-  \node [above=5mm of 0]
-  {\makebox[0mm]{\footnotesize
-      \begin{tabular}{@{}l@{}}input\\[-1mm]program\end{tabular}}}; 
-     
-  \node (A) at (0,0)  [node] {};
-  \node [below right] at (A.north west) {lexer};
-
-  \node (B) at (3,0)  [node] {};
-  \node [below right=1mm] at (B.north west) {\mbox{}\hspace{-1mm}parser};
-
-  \node (C) at (6,0)  [node] {};
-  \node [below right] at (C.north west) {\mbox{}\hspace{-1mm}code gen};
-
-  \node (1) at (8.4,0) {};
-  \node [above=5mm of 1]
-  {\makebox[0mm]{\footnotesize
-      \begin{tabular}{@{}r@{}}binary\\[-1mm]code\end{tabular}}};
-
-  \draw [->,line width=4mm] (0) -- (A); 
-  \draw [->,line width=4mm] (A) -- (B); 
-  \draw [->,line width=4mm] (B) -- (C); 
-  \draw [->,line width=4mm] (C) -- (1); 
-  \end{tikzpicture}
-  \end{center}
-
-\only<2,3,4>{
-\begin{textblock}{1}(1,2.1)
-\begin{bubble}[9.8cm]
-\normalsize
-lexer input: a string\smallskip\\
-\hspace{5mm}\code{"read(n);"}\medskip\\
-lexer output: a sequence of tokens\smallskip\\
-\hspace{5mm}\code{key(read) lpar id(n) rpar semi}
-\end{bubble}
-\end{textblock}}
-
-\only<3,4>{
-\begin{textblock}{1}(6,7.8)
-\begin{tabular}{c}
-\includegraphics[scale=0.2]{rosetta.jpg}\\[-2mm]
-\footnotesize lexing $\Rightarrow$ recognising words (Stone of Rosetta)
-\end{tabular}
-\end{textblock}}
-
-\only<4>{
-\begin{textblock}{1}(0.5,12)\small
-\begin{tabular}{l@{}c@{}l}
-  \pcode{if}    & $\;\Rightarrow\;$ & keyword\\
-  \pcode{iffoo} & $\;\Rightarrow\;$ & identifier\\
-\end{tabular}  
-\end{textblock}}
+\begin{tikzpicture}
+\begin{semilogyaxis}[
+    xlabel={$n$},
+    x label style={at={(1.05,0.0)}},   
+    ylabel={regex size},
+    enlargelimits=false,
+    xtick={1,4,...,30},
+    xmax=33,
+    %ytick={0, 10,...,100},
+    scaled ticks=false,
+    axis lines=left,
+    width=9cm,
+    height=4.5cm, 
+    legend entries={Simple Scala},  
+    legend pos=  south east,
+    legend cell align=left  
+]
+\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
+%\addplot[brown,mark=pentagon*, mark options={fill=white}] table {re-ssize.data};  
+%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};  
+%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
+\end{semilogyaxis}
+\end{tikzpicture}
+\end{center}
+Regex: \bl{$(a+aa)^* \cdot b$} \space\space\space\space\space\space
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}\\
+\begin{itemize}
+\item
+Solution: Simplification%(Sulzmann \& Lu)
+\begin{itemize}
+\item $r+(r+s) = r+r+s = r+s$
+\item $1 \cdot r= r$
+\end{itemize}
+\end{itemize}
+\end{frame}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}[t]
+\frametitle{Optimization}
 
-\only<5>{
-\begin{textblock}{1}(1,1.5)
-\begin{bubble}[8.5cm]
-\normalsize
-parser input: a sequence of tokens\smallskip\\
-
-{\small\hspace{5mm}\code{key(read) lpar id(n) rpar semi}}\smallskip\\
-
-parser output: an abstract syntax tree\smallskip\\
-\footnotesize
-\hspace{2cm}\begin{tikzpicture}
-  \node {\code{read}}
-    child {node {\code{lpar}}}
-    child {node {\code{n}}}
-    child {node {\code{rpar}}};
-\end{tikzpicture}
-\end{bubble}
-\end{textblock}}
+Regex: \bl{$(a+aa)^* \cdot b$} \space\space\space\space\space\space
+Strings of the form \bl{$\underbrace{\,a\ldots a\,}_{n}$}
 
-\only<6,7>{
-\begin{textblock}{1}(1,1.5)
-\begin{bubble}[4cm]
-\normalsize
-code generator:\smallskip\\
-\hspace{5mm}\code{istore 2}\\ 
-\hspace{5mm}\code{iload 2}\\ 
-\hspace{5mm}\code{ldc 10}\\
-\hspace{5mm}\code{isub}\\
-\hspace{5mm}\code{ifeq Label2}\\ 
-\hspace{5mm}\code{iload 2}\\
-\hspace{5mm}\code{...}\\
-\end{bubble}
-\end{textblock}}
-
-\only<7>{
-\begin{textblock}{6}(8.4,7)
-\begin{bubble}[5cm]
-\mbox{\begin{tikzpicture}[scale=0.58,rounded corners=0mm]
-\begin{axis}[axis x line=bottom, axis y line=left, ylabel=secs,
-    xlabel=n,
-    enlargelimits=0.05,
-    ybar interval=0.7, legend style=small]
-\addplot file {interpreted2.data};
-\addplot file {compiled2.data};
-%\legend{interpreted, compiled}
+\begin{center}
+\begin{tikzpicture}
+\begin{axis}[
+    xlabel={$n$},
+    x label style={at={(1.05,0.0)}},   
+    ylabel={regex size},
+    enlargelimits=false,
+    xtick={1,4,...,30},
+    xmax=33,
+    %ytick={0, 10,...,100},
+    scaled ticks=false,
+    axis lines=left,
+    width=9cm,
+    height=4.5cm, 
+    legend entries={Simplification Applied},  
+    legend pos=  south east,
+    legend cell align=left  
+]
+%\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
+\addplot[black,mark=triangle*, mark options={fill=white}] table {re-ssize.data};  
+%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};  
+%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
 \end{axis}
-\end{tikzpicture}}
-\end{bubble}
-\end{textblock}}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{The Acad.~Subject is Mature}
-
+\end{tikzpicture}
+\end{center}
 \begin{itemize}
-\item Turing Machines, 1936
-\item Regular Expressions, 1956\\
-\item The first compiler for COBOL, 1957\\ (Grace Hopper)
-\item But surprisingly research papers are still published nowadays\\
-\item ``Parsing: The Solved Problem That Isn't''
+\item
+Lexer? Not just matcher
+\begin{itemize}
+\item
+Bit-Coded Regular Expression Parsing (Lasse Nielsen, Fritz Henglein 2011)
+\item
+Bit-Coded Regular Expression Parsing with Simplification (Sulzmann and Lu 2014)
 \end{itemize}
 
-\begin{flushright}
-\includegraphics[scale=0.3]{hopper.jpg}\\
-\footnotesize\textcolor{gray}{Grace Hopper}
-\end{flushright}
+\end{itemize}
+\end{frame}
 
 
-\begin{flushright}
-\mbox{}\\[-6mm]
-{\footnotesize\textcolor{gray}{(she made it to David Letterman's Tonight Show,\\[-2mm]
- \url{http://www.youtube.com/watch?v=aZOxtURhfEU})}}
-\end{flushright}
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%     
 
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Lectures 1 - 5}
 
-transforming strings into structured data\\[10mm]
-
-{\LARGE\bf Lexing} {\hfill{}based on regular expressions}\medskip\\
-\hspace{5mm}(recognising ``words'')\\[6mm]
-
-{\LARGE\bf Parsing}\medskip\\
-\hspace{5mm}(recognising ``sentences'')
-
-\begin{textblock}{1}(10,9.1)
-\begin{tabular}{c}
-\includegraphics[scale=0.1]{rosetta.jpg}\\[-2mm]
-\footnotesize Stone of Rosetta
-\end{tabular}
-\end{textblock}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}[t]
-\frametitle{Familiar Regular Expr.}
-\small
-\begin{center}
-\texttt{[a-z0-9\_$\backslash{}$.-]+ @ [a-z0-9$\backslash{}$.-]+ . [a-z$\backslash{}$.]\{2,6\}}
-\end{center}\smallskip
-
-\begin{center}
-\begin{tabular}{@{}lp{8.5cm}@{}}
-\pcode{re*} & matches 0 or more times\\
-\pcode{re+} & matches 1 or more times\\
-\pcode{re?} & matches 0 or 1 times\\
-\pcode{re\{n\}}	& matches exactly \pcode{n} number of times\\
-\pcode{re\{n,m\}} & matches at least \pcode{n} and at most {\tt m} times\\
-\pcode{[...]} & matches any single character inside the brackets\\
-\pcode{[^...]} & matches any single character not inside the 
-brackets\\
-\pcode{a-z A-Z} & character ranges\\
-\pcode{\\d} & matches digits; equivalent to \pcode{[0-9]}\\
-\pcode{.} & matches every character except newline\\
-\pcode{(re)}	& groups regular expressions and remembers 
-the matched text
-\end{tabular}
-\end{center}
+\frametitle{Ongoing Work}
 
 
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Today}
-
-\begin{itemize}
-\item While the ultimate goal is to implement a small compiler for the JVM
-  \ldots\bigskip
-\end{itemize}
-
-Let's start with:
+\begin{tikzpicture}
+\begin{semilogyaxis}[
+    xlabel={$n$},
+    x label style={at={(1.05,0.0)}},   
+    ylabel={regex size},
+    enlargelimits=false,
+    xtick={1,4,...,30},
+    xmax=33,
+    %ytick={0, 10,...,100},
+    scaled ticks=false,
+    axis lines=left,
+    width=9cm,
+    height=4.5cm, 
+    legend entries={Naive, Simp},  
+    legend pos= north west,
+    legend cell align=left  
+]
+\addplot[black,mark=square*, mark options={fill=white}] table {re-usize.data};
+\addplot[black,mark=triangle*, mark options={fill=white}] table {re-ssize.data};  
+%\addplot[red,mark=triangle*,mark options={fill=white}] table {re1.data};  
+%\addplot[green,mark=square*,mark options={fill=white}] table {re2.data};
+\end{semilogyaxis}
+\end{tikzpicture}
 
 \begin{itemize}
-\item a web-crawler
-\item an email harvester
-%\item \textcolor{gray}{(a web-scraper)}
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
+\item
+Correctness of Sulzmann \& Lu's algorithm
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{A Web-Crawler}
-
-\mbox{}\\[10mm]
-
-\begin{enumerate}
-\item given an URL, read the corresponding webpage
-\item extract all links from it
-\item call the web-crawler again for all these links
-\end{enumerate}
-
+\item
+Size Bound $O(n^2t^2)$ of Dervatives (1995 Antimirov "Partial Derivative")
+\item
+More radical simplifications.
+\item
+Extend the algorithm to back-references.
+\end{itemize}
 \end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{A Web-Crawler}
-
-\mbox{}\\[10mm]
-
-
-\begin{enumerate}
-\item given an URL, read the corresponding webpage
-\item if not possible print, out a problem
-\item if possible, extract all links from it
-\item call the web-crawler again for all these links
-\end{enumerate}\bigskip\pause
-
-\small (we need a bound for the number of recursive calls)
-
-\small (the purpose is to check all links on my own webpage)
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-
-\begin{textblock}{1}(2,5)
-\begin{tabular}{c}
-\includegraphics[scale=0.15]{servers.png}\\[-2mm]
-\small Server
-\end{tabular}
-\end{textblock}
-
-\begin{textblock}{1}(5.6,4)
-  \begin{tikzpicture}[scale=1.1]
-  \draw[white] (0,1) node (X) {};
-  \draw[white] (2,1) node (Y) {};
-   \draw[white] (0,0) node (X1) {};
-  \draw[white] (2,0) node (Y1) {};
-   \draw[white] (0,-1) node (X2) {};
-  \draw[white] (2,-1) node (Y2) {};
-  \draw[red, <-, line width = 2mm] (X) -- (Y);
-  \node [inner sep=5pt,label=above:\textcolor{black}{GET request}] at ($ (X)!.5!(Y) $) {};
-  \draw[red, ->, line width = 2mm] (X1) -- (Y1);
-  \node [inner sep=5pt,label=above:\textcolor{black}{webpage}] at ($ (X1)!.5!(Y1) $) {};
-  \draw[red, <-, line width = 2mm] (X2) -- (Y2);
-  \node [inner sep=7pt,label=above:\textcolor{black}{POST data}] at ($ (X2)!.5!(Y2) $) {};
-  \end{tikzpicture}
-\end{textblock}
 
 
-\begin{textblock}{1}(9,5.5)
-\begin{tabular}{c}
-\includegraphics[scale=0.15]{laptop.png}\\[-2mm]
-\small Browser
-\end{tabular}
-\end{textblock}
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-  
-
- 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{A Regular Expression}
-
-\begin{itemize}
-\item \ldots{} is a pattern or template for specifying strings
-\end{itemize}\bigskip
-  
-\begin{center}  
-\only<1>{\scode{"https?://[^"]*"}}%
-\only<2>{\scode{""""https?://[^"]*"""".r}}
-\end{center}\bigskip\bigskip
-
-matches for example\smallskip\\  
-\hspace{2mm}\code{"http://www.foobar.com"}\\
-\hspace{2mm}\code{"https://www.tls.org"}\smallskip\\
-
-but not\smallskip\\  
-\hspace{2mm}\code{"http://www."foo"bar.com"}\\
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Finding Operations in Scala}
-
-{\bf\code{rexp.findAllIn(string)}}\medskip
-  
-returns a list of all (sub)strings that match the 
-regular expression
-\bigskip\bigskip  
-  
-
-{\bf\code{rexp.findFirstIn(string)}}\medskip
- 
-returns either 
-
-\begin{itemize}
-\item \code{None} if no (sub)string matches or 
-\item \code{Some(s)} with the first (sub)string
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Regular Expressions}
-
-Their inductive definition:
 
 
-\begin{textblock}{6}(2,7.5)
-  \begin{tabular}{@ {}rrl@ {\hspace{13mm}}l}
-  \bl{$r$} & \bl{$::=$}  & \bl{$\ZERO$}  & nothing\\
-         & \bl{$\mid$} & \bl{$\ONE$}       & empty string / \pcode{""} / $[]$\\
-         & \bl{$\mid$} & \bl{$c$}                         & character\\
-         & \bl{$\mid$} & \bl{$r_1 + r_2$}  & alternative / choice\\
-         & \bl{$\mid$} & \bl{$r_1 \cdot r_2$} & sequence\\
-         & \bl{$\mid$} & \bl{$r^*$}            & star (zero or more)\\
-  \end{tabular}
-  \end{textblock}
-  
-  
-  
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%\begin{frame}[t]
-%\frametitle{Regular Expressions}
-%
-%\small
-%In Scala:\bigskip
-%
-%\footnotesize
-%\lstinputlisting{../progs/app51.scala}
-%
-%  
-%\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Strings}
-
-\ldots are lists of characters. For example \code{"hello"}
-
-\begin{center}
-\bl{$[h, e, l, l, o]$} or just \bl{$hello$}
-\end{center}
-
-the empty string: \bl{$[]$} or \bl{\pcode{""}}\bigskip\\
-
-the concatenation of two strings:
-
-\begin{center}
-\bl{$s_1 \,@\, s_2$}
-\end{center}
-
-\bl{\textit{foo $@$ bar = foobar}, \textit{baz $@\, []$ = baz}}
-  
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Languages, Strings}
-
-\begin{itemize}
-\item \alert{\bf Strings} are lists of characters, for example
-\begin{center}
-\bl{$[]$},\;\bl{$abc$}  \hspace{2cm}(Pattern match: \bl{$c\!::\!s$})
-\end{center}\bigskip
-
-
-\item A \alert{\bf language} is a set of strings, for example\medskip
-\begin{center}
-\bl{$\{[], hello, \textit{foobar}, a, abc\}$}
-\end{center}\bigskip
-
-\item \alert{\bf Concatenation} of strings and languages
-
-\begin{center}
-\begin{tabular}{rcl}
-\bl{$\textit{foo}\;@\;bar$} & \bl{$=$} & \bl{$\textit{foobar}$}\medskip\\
-\bl{$A\;@\;B$} & \bl{$\dn$} & \bl{$\{ s_1\,@\,s_2 \;\mid\; s_1 \in A \wedge s_2 \in B\}$}
-\end{tabular}
-\end{center}
-
-%\item The \alert{\bf meaning} of a regular expression is a set of 
-%  strings, or language.
-\end{itemize}  
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}The Meaning of a\\[-2mm] 
-  Regular Expression\end{tabular}}
 
-\begin{textblock}{15}(1,4)
- \begin{tabular}{rcl}
- \bl{$L(\ZERO)$}  & \bl{$\dn$} & \bl{$\{\}$}\\
- \bl{$L(\ONE)$}     & \bl{$\dn$} & \bl{$\{[]\}$}\\
- \bl{$L(c)$}            & \bl{$\dn$} & \bl{$\{[c]\}$}\\
- \bl{$L(r_1 + r_2)$}    & \bl{$\dn$} & \bl{$L(r_1) \cup L(r_2)$}\\
- \bl{$L(r_1 \cdot r_2)$} & \bl{$\dn$} & \bl{$\{ s_1 \,@\, s_2 \;|\; s_1 \in L(r_1) \wedge s_2 \in L(r_2) \}$}\\
- \bl{$L(r^*)$}           & \bl{$\dn$} & \onslide<4->{\bl{$\bigcup_{0 \le n} L(r)^n$}}\\
-  \end{tabular}\bigskip
-  
-\onslide<2->{
-\hspace{5mm}\bl{$L(r)^0 \;\dn\; \{[]\}$}\\
-\bl{$L(r)^{n+1} \;\dn\; L(r) \,@\, L(r)^n$}\hspace{9mm}\onslide<3->{\small\textcolor{gray}{(append on sets)}\\
-\small\hspace{5cm}\textcolor{gray}{$\{ s_1 @ s_2 \;|\; s_1\in L(r) \wedge s_2 \in L(r)^n \}$}}
-}  
-    \end{textblock}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{The Meaning of Matching}
-
-\begin{bubble}[10cm]
-\large\bf 
-A regular expression \bl{$r$} matches a string~\bl{$s$} 
-provided
-
-\begin{center}
-\bl{$s \in L(r)$}\\ 
-\end{center}
-\end{bubble}\bigskip\bigskip
-
-\ldots and the point of the next lecture is 
-to decide this problem as fast as possible (unlike Python,
-Ruby, Java)
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Written Exam}
-
-\begin{itemize}
-\item Accounts for 80\%.\bigskip
-
-\item The question ``\textit{Is this relevant for
-      the exam?}'' is very demotivating for the lecturer!\bigskip\\
-
-\item Deal: Whatever is in the homework (and is not marked
-      ``\textit{optional}'') is relevant for the exam.\bigskip
-      
-\item Each lecture has also a handout. There are also handouts about
-notation and Scala.      
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[t]
-\frametitle{Coursework}
-
-\begin{itemize}
-\item Accounts for 20\%. Two strands. Choose \alert{\bf one}!\bigskip
-\end{itemize}
-
-\begin{columns}[t]
-\begin{column}{.5\textwidth}
-\underline{\bf Strand 1}\medskip
-\begin{itemize}
-\item four programming tasks:
-\begin{itemize}
-\item matcher (4\%, 12.10.) 
-\item lexer (5\%, 02.11.)
-\item parser (5\%, 23.11.)
-\item compiler (6\%, 14.12.)
-\end{itemize}
-\item in any lang.~you like,\\ but I want to see the code
-\end{itemize}
-\end{column}
-
-\hspace{-45pt}\vrule{}\hspace{10pt}
-\begin{column}{.5\textwidth}
-\underline{\bf Strand 2}\smallskip\begin{itemize}
-\item one task: prove the correctness of a regular expression matcher in 
-the \underline{Isabelle} theorem prover
-\item 20\%, submission on~14.12.\hspace{-5mm}\mbox{}
-\end{itemize}
-\end{column}
-\end{columns}\medskip
-
-\small
-\begin{itemize}
-\item Solving more than one strand will {\bf not} give you more 
-marks.
-
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}[c]
-\frametitle{Lecture Capture}
-
-\begin{itemize}
-\item Hope it works\ldots\pause actually no, it does not!\medskip\pause
-\item It is important to use lecture capture wisely\\ (it is only the ``baseline''):
-\begin{itemize}  
-\item Lecture recordings are a study and revision aid.
-\item Statistically, there is a clear and direct link between attendance and
-  attainment: Students who do not attend lectures, do less well in exams.
-\end{itemize}
-
-\item Attending a lecture is more than watching it online -- if you do not
-attend, you miss out!  
-  
-\end{itemize}
-
-\end{frame}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




