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+++ b/slides/slides06.tex Sat Jun 15 09:23:18 2013 -0400
@@ -0,0 +1,579 @@
+\documentclass[dvipsnames,14pt,t]{beamer}
+\usepackage{beamerthemeplainculight}
+\usepackage[T1]{fontenc}
+\usepackage[latin1]{inputenc}
+\usepackage{mathpartir}
+\usepackage[absolute,overlay]{textpos}
+\usepackage{ifthen}
+\usepackage{tikz}
+\usepackage{pgf}
+\usepackage{calc}
+\usepackage{ulem}
+\usepackage{courier}
+\usepackage{listings}
+\renewcommand{\uline}[1]{#1}
+\usetikzlibrary{arrows}
+\usetikzlibrary{automata}
+\usetikzlibrary{shapes}
+\usetikzlibrary{shadows}
+\usetikzlibrary{positioning}
+\usetikzlibrary{calc}
+\usetikzlibrary{plotmarks}
+\usepackage{graphicx}
+
+\definecolor{javared}{rgb}{0.6,0,0} % for strings
+\definecolor{javagreen}{rgb}{0.25,0.5,0.35} % comments
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+\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
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+\lstset{language=Java,
+ basicstyle=\ttfamily,
+ keywordstyle=\color{javapurple}\bfseries,
+ stringstyle=\color{javagreen},
+ commentstyle=\color{javagreen},
+ morecomment=[s][\color{javadocblue}]{/**}{*/},
+ numbers=left,
+ numberstyle=\tiny\color{black},
+ stepnumber=1,
+ numbersep=10pt,
+ tabsize=2,
+ showspaces=false,
+ showstringspaces=false}
+
+\lstdefinelanguage{scala}{
+ morekeywords={abstract,case,catch,class,def,%
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+ morestring=[b]",
+ morestring=[b]',
+ morestring=[b]"""
+}
+
+\lstset{language=Scala,
+ basicstyle=\ttfamily,
+ keywordstyle=\color{javapurple}\bfseries,
+ stringstyle=\color{javagreen},
+ commentstyle=\color{javagreen},
+ morecomment=[s][\color{javadocblue}]{/**}{*/},
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+ stepnumber=1,
+ numbersep=10pt,
+ tabsize=2,
+ showspaces=false,
+ showstringspaces=false}
+
+% beamer stuff
+\renewcommand{\slidecaption}{AFL 06, King's College London, 31.~October 2012}
+\newcommand{\bl}[1]{\textcolor{blue}{#1}}
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+
+
+% The data files, written on the first run.
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+\end{filecontents}
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}<1>[t]
+\frametitle{%
+ \begin{tabular}{@ {}c@ {}}
+ \\[-3mm]
+ \LARGE Automata and \\[-2mm]
+ \LARGE Formal Languages (6)\\[3mm]
+ \end{tabular}}
+
+ \normalsize
+ \begin{center}
+ \begin{tabular}{ll}
+ Email: & christian.urban at kcl.ac.uk\\
+ Of$\!$fice: & S1.27 (1st floor Strand Building)\\
+ Slides: & KEATS (also home work is there)\\
+ \end{tabular}
+ \end{center}
+
+
+\end{frame}}
+ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+``I hate coding. I do not want to look at code.''
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+``I am appalled. You do not show code anymore.''
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}ReDoS\end{tabular}}
+
+\begin{itemize}
+\item \alert{R}egular \alert{e}xpression \alert{D}enial \alert{o}f \alert{S}ervice\bigskip
+\item ``Regular Expressions Will Stab You in the Back''\bigskip
+\item Evil regular expressions\medskip
+\begin{itemize}
+\item \bl{$(a?\{n\})a\{n\}$}
+\item \bl{$(a^+)^+$}
+\item \bl{$([a-zA-Z]^+)^*$}
+\item \bl{$(a + aa)^+$}
+\item \bl{$(a + a?)^+$}
+\end{itemize}
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Regexp Matching\end{tabular}}
+
+Given a regular expression
+
+\begin{enumerate}
+\item you might convert it into a DFA (subset construction)
+\item you might try all possible paths in an NFA via backtracking
+\item you might try all paths in an NFA in parallel
+\item you might try to convert the DFA ``lazily''
+\end{enumerate}\bigskip
+
+Often No~2 is implemented (sometimes there are even good reasons for doing this).
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}\bl{$(a?\{n\})a\{n\}$} in Python\end{tabular}}
+
+\begin{tikzpicture}[y=.2cm, x=.3cm]
+ %axis
+ \draw (0,0) -- coordinate (x axis mid) (30,0);
+ \draw (0,0) -- coordinate (y axis mid) (0,30);
+ %ticks
+ \foreach \x in {0,5,...,30}
+ \draw (\x,1pt) -- (\x,-3pt)
+ node[anchor=north] {\x};
+ \foreach \y in {0,5,...,30}
+ \draw (1pt,\y) -- (-3pt,\y)
+ node[anchor=east] {\y};
+ %labels
+ \node[below=0.6cm] at (x axis mid) {\bl{a}s};
+ \node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+ %plots
+ \draw[color=blue] plot[mark=*, mark options={fill=white}]
+ file {re-python.data};
+ \only<2->{
+ \draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
+ file {re1.data};}
+ \only<3->{
+ \draw[color=green] plot[mark=square*, mark options={fill=white} ]
+ file {re2.data};}
+
+ %legend
+ \begin{scope}[shift={(4,20)}]
+ \draw[color=blue] (0,0) --
+ plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small Python};
+ \only<2->{\draw[yshift=\baselineskip, color=red] (0,0) --
+ plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small Scala V1};}
+ \only<3->{
+ \draw[yshift=2\baselineskip, color=green] (0,0) --
+ plot[mark=square*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small Scala V2 with simplifications};}
+ \end{scope}
+\end{tikzpicture}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+
+
+\begin{tikzpicture}[y=.7cm, x=.0009cm]
+ %axis
+ \draw (0,0) -- coordinate (x axis mid) (10000,0);
+ \draw (0,0) -- coordinate (y axis mid) (0,6);
+ %ticks
+ \foreach \x in {0,2000,...,10000}
+ \draw (\x,1pt) -- (\x,-3pt)
+ node[anchor=north] {\x};
+ \foreach \y in {0,1,...,6}
+ \draw (1pt,\y) -- (-3pt,\y)
+ node[anchor=east] {\y};
+ %labels
+ \node[below=0.6cm] at (x axis mid) {\bl{a}s};
+ \node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+ %plots
+ \draw[color=blue] plot[mark=*, mark options={fill=white}]
+ file {re-internal.data};
+ \only<2->{
+ \draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
+ file {re3.data};}
+
+ %legend
+ \begin{scope}[shift={(2000,4)}]
+ \draw[color=blue] (0,0) --
+ plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small Scala Internal};
+ \only<2->{
+ \draw[yshift=\baselineskip, color=red] (0,0) --
+ plot[mark=triangle*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small Scala V3 with explicit $\_\{\_\}$};}
+ \end{scope}
+\end{tikzpicture}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+\newcommand{\qq}{\mbox{\texttt{"}}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Grammars\end{tabular}}
+
+A (context-free) grammar \bl{$G$} consists of
+
+\begin{itemize}
+\item a finite set of nonterminal symbols (upper case)
+\item a finite terminal symbols or tokens (lower case)
+\item a start symbol (which must be a nonterminal)
+\item a set of rules
+\begin{center}
+\bl{$A \rightarrow \text{rhs}$}
+\end{center}
+
+where \bl{rhs} are sequences involving terminals and nonterminals.\medskip\pause
+
+We can also allow rules
+\begin{center}
+\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
+\end{center}
+\end{itemize}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Palindromes\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$S$ & $\rightarrow$ & $\epsilon$ \\
+$S$ & $\rightarrow$ & $a\cdot S\cdot a$ \\
+$S$ & $\rightarrow$ & $b\cdot S\cdot b$ \\
+\end{tabular}}
+\end{center}\pause
+
+or
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$S$ & $\rightarrow$ & $\epsilon \;|\; a\cdot S\cdot a \;|\;b\cdot S\cdot b$ \\
+\end{tabular}}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ & $num\_token$ \\
+$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ & $( \cdot E \cdot )$
+\end{tabular}}
+\end{center}\pause
+
+\bl{\texttt{1 + 2 * 3 + 4}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Parse Trees\end{tabular}}
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ & $F \;|\; F \cdot * \cdot F$\\
+$F$ & $\rightarrow$ & $T \;|\; T \cdot + \cdot T \;|\; T \cdot - \cdot T$\\
+$T$ & $\rightarrow$ & $num\_token \;|\; ( \cdot E \cdot )$\\
+\end{tabular}}
+\end{center}
+
+\begin{center}
+\begin{tikzpicture}[level distance=8mm, blue]
+ \node {$E$}
+ child {node {$F$}
+ child {node {$T$}
+ child {node {(\,$E$\,)}
+ child {node{$F$ *{} $F$}
+ child {node {$T$} child {node {2}}}
+ child {node {$T$} child {node {3}}}
+ }
+ }
+ }
+ child {node {+}}
+ child {node {$T$}
+ child {node {(\,$E$\,)}
+ child {node {$F$}
+ child {node {$T$ +{} $T$}
+ child {node {3}}
+ child {node {4}}
+ }
+ }}
+ }};
+\end{tikzpicture}
+\end{center}
+
+\begin{textblock}{5}(1, 6.5)
+\bl{\texttt{(2*3)+(3+4)}}
+\end{textblock}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
+
+A grammar is \alert{ambiguous} if there is a string that has at least parse trees.
+
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$E$ & $\rightarrow$ & $num\_token$ \\
+$E$ & $\rightarrow$ & $E \cdot + \cdot E$ \\
+$E$ & $\rightarrow$ & $E \cdot - \cdot E$ \\
+$E$ & $\rightarrow$ & $E \cdot * \cdot E$ \\
+$E$ & $\rightarrow$ & $( \cdot E \cdot )$
+\end{tabular}}
+\end{center}
+
+\bl{\texttt{1 + 2 * 3 + 4}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}}
+
+All rules must be of the form
+
+\begin{center}
+\bl{$A \rightarrow a$}
+\end{center}
+
+or
+
+\begin{center}
+\bl{$A \rightarrow B\cdot C$}
+\end{center}
+
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
+
+
+\begin{center}
+\bl{\begin{tabular}{@ {}lcl}
+$S$ & $\rightarrow$ & $N\cdot P$ \\
+$P$ & $\rightarrow$ & $V\cdot N$ \\
+$N$ & $\rightarrow$ & $N\cdot N$ \\
+$N$ & $\rightarrow$ & $\texttt{students} \;|\; \texttt{Jeff} \;|\; \texttt{geometry} \;|\; \texttt{trains} $ \\
+$V$ & $\rightarrow$ & $\texttt{trains}$
+\end{tabular}}
+\end{center}
+
+\bl{\texttt{Jeff trains geometry students}}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[c]
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
+
+
+\begin{itemize}
+\item runtime is \bl{$O(n^3)$}\bigskip
+\item grammars need to be transferred into CNF
+\end{itemize}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
+