--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/slides08.tex Tue Nov 20 22:06:05 2012 +0000
@@ -0,0 +1,227 @@
+\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
+\definecolor{javapurple}{rgb}{0.5,0,0.35} % keywords
+\definecolor{javadocblue}{rgb}{0.25,0.35,0.75} % javadoc
+
+\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,%
+ do,else,extends,false,final,finally,%
+ for,if,implicit,import,match,mixin,%
+ new,null,object,override,package,%
+ private,protected,requires,return,sealed,%
+ super,this,throw,trait,true,try,%
+ type,val,var,while,with,yield},
+ otherkeywords={=>,<-,<\%,<:,>:,\#,@},
+ sensitive=true,
+ morecomment=[l]{//},
+ morecomment=[n]{/*}{*/},
+ 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}]{/**}{*/},
+ numbers=left,
+ numberstyle=\tiny\color{black},
+ stepnumber=1,
+ numbersep=10pt,
+ tabsize=2,
+ showspaces=false,
+ showstringspaces=false}
+
+% beamer stuff
+\renewcommand{\slidecaption}{AFL 08, King's College London, 21.~November 2012}
+\newcommand{\bl}[1]{\textcolor{blue}{#1}}
+\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
+
+
+% The data files, written on the first run.
+\begin{filecontents}{s-grammar1.data}
+1 0.01152
+51 0.07973
+101 0.09726
+151 0.09320
+201 0.10010
+251 0.16997
+301 0.26662
+351 0.46118
+401 0.62516
+451 0.87247
+501 1.16334
+551 1.71152
+601 2.10958
+651 2.44360
+701 2.98488
+751 3.50326
+801 4.11036
+851 4.93394
+901 5.77465
+951 7.39123
+\end{filecontents}
+
+\begin{filecontents}{s-grammar2.data}
+1 0.01280
+2 0.00064
+3 0.00173
+4 0.00355
+5 0.00965
+6 0.02674
+7 0.06953
+8 0.11166
+9 0.18707
+10 0.09189
+11 0.12724
+12 0.24337
+13 0.59304
+14 1.53594
+15 4.01195
+16 10.73582
+17 29.51587
+#18 73.14163
+\end{filecontents}
+
+
+\begin{document}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}<1>[t]
+\frametitle{%
+ \begin{tabular}{@ {}c@ {}}
+ \\[-3mm]
+ \LARGE Automata and \\[-2mm]
+ \LARGE Formal Languages (8)\\[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]
+\frametitle{\begin{tabular}{c}Two Grammars\end{tabular}}
+
+Which languages are recognised by the following two grammars?
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$S$ & $\rightarrow$ & $1 \cdot S \cdot S$\\
+ & $|$ & $\epsilon$
+\end{tabular}}
+\end{center}\bigskip
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$U$ & $\rightarrow$ & $1 \cdot U$\\
+ & $|$ & $\epsilon$
+\end{tabular}}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}Ambiguous Grammars\end{tabular}}
+
+\mbox{}\\[-25mm]\mbox{}
+
+\begin{center}
+\begin{tikzpicture}[y=.2cm, x=.009cm]
+ %axis
+ \draw (0,0) -- coordinate (x axis mid) (1000,0);
+ \draw (0,0) -- coordinate (y axis mid) (0,30);
+ %ticks
+ \foreach \x in {0, 20, 100, 200,...,1000}
+ \draw (\x,1pt) -- (\x,-3pt)
+ node[anchor=north] {\small \x};
+ \foreach \y in {0,5,...,30}
+ \draw (1pt,\y) -- (-3pt,\y)
+ node[anchor=east] {\small\y};
+ %labels
+ \node[below=0.6cm] at (x axis mid) {\bl{1}s};
+ \node[rotate=90, left=1.2cm] at (y axis mid) {secs};
+
+ %plots
+ \draw[color=blue] plot[mark=*, mark options={fill=white}]
+ file {s-grammar1.data};
+ \only<2->{\draw[color=red] plot[mark=triangle*, mark options={fill=white} ]
+ file {s-grammar2.data};}
+ %legend
+ \begin{scope}[shift={(400,20)}]
+ \draw[color=blue] (0,0) --
+ plot[mark=*, mark options={fill=white}] (0.25,0) -- (0.5,0)
+ node[right]{\small unambiguous};
+ \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 ambiguous};}
+ \end{scope}
+\end{tikzpicture}
+\end{center}
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+\end{document}
+
+%%% Local Variables:
+%%% mode: latex
+%%% TeX-master: t
+%%% End:
+