
diff -r e85600529ca5 -r 4794759139ea slides07.tex
--- a/slides07.tex	Sat Jun 15 09:11:11 2013 -0400
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,542 +0,0 @@
-\documentclass[dvipsnames,14pt,t]{beamer}
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-\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}
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-\usepackage{graphicx} 
-
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-% beamer stuff 
-\renewcommand{\slidecaption}{AFL 07, King's College London, 14.~November 2012}
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-\begin{document}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}<1>[t]
-\frametitle{%
-  \begin{tabular}{@ {}c@ {}}
-  \\[-3mm]
-  \LARGE Automata and \\[-2mm] 
-  \LARGE Formal Languages (7)\\[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}[t]
-\frametitle{\begin{tabular}{c}\bl{$(a?\{n\})a\{n\}$}\end{tabular}}
-
-\mbox{}\\[-13mm]
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-\begin{tikzpicture}[y=.2cm, x=.3cm]
- 	%axis
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-     		\draw (1pt,\y) -- (-3pt,\y) 
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-	%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};
-	\draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 
-		file {re1.data};
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-		file {re2.data};
-         \draw[color=brown] plot[mark=pentagon*, mark options={fill=white} ] 
-		file {re-ruby.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};
-	\draw[yshift=-\baselineskip, color=brown] (0,0) -- 
-		plot[mark=pentagon*, mark options={fill=white}] (0.25,0) -- (0.5,0)
-		node[right]{\small Ruby (Daniel Baldwin)};
-         \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};	
-	 \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}[t]
-
-\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);
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-    	\foreach \x in {0,2000,...,10000}
-     		\draw (\x,1pt) -- (\x,-3pt)
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-	%plots
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-		file {re-internal.data};
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-         \draw[color=red] plot[mark=triangle*, mark options={fill=white} ] 
-		file {re3.data};}
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-	\draw[color=blue] (0,0) -- 
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-		node[right]{\small Scala Internal};
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-	\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 $\_\{\_\}$};}
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-\end{tikzpicture}
-
-\begin{center}
-\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {\hspace{-10mm}}l@ {}}
-  \\[-8mm]
-  \bl{der c (r$_1$ $\cdot$ r$_2$)} & \bl{$\dn$}  & \bl{if nullable r$_1$}\\
-  & & \bl{then ((der c r$_1$) $\cdot$ r$_2$) + (der c r$_2$)}\\ 
-  & & \bl{else (der c r$_1$) $\cdot$ r$_2$}\\
-  \bl{der c (r$\{n\}$)} & \bl{$\dn$} & \bl{if $n = 0$ then $\varnothing$}\\
-  & & \bl{else (der c r) $\cdot$ r$\{n - 1\}$}
-  \end{tabular}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-
-
-\newcommand{\qq}{\mbox{\texttt{"}}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}CFGs\end{tabular}}
-
-A \alert{context-free} grammar (CFG) \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 (can also be empty).\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}A CFG Derivation\end{tabular}}
-
-\begin{enumerate}
-\item Begin with a string with only the start symbol \bl{$S$}\bigskip
-\item Replace any non-terminal \bl{$X$} in the string by the
right-hand side of some production \bl{$X \rightarrow \text{rhs}$}\bigskip
-\item Repeat 2 until there are no non-terminals
-\end{enumerate}
-
-\begin{center}
-\bl{$S \rightarrow \ldots \rightarrow \ldots  \rightarrow \ldots  \rightarrow \ldots $}
-\end{center}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Language of a CFG\end{tabular}}
-
-Let \bl{$G$} be a context-free grammar with start symbol \bl{$S$}. 
-Then the language \bl{$L(G)$} is:
-
-\begin{center}
-\bl{$\{c_1\ldots c_n \;|\; \forall i.\; c_i \in T \wedge S \rightarrow^* c_1\ldots c_n \}$}
-\end{center}\pause
-
-\begin{itemize}
-\item Terminals are so-called because there are no rules for replacing them
-\item Once generated, terminals are ``permanent''
-\item Terminals ought to be tokens of the language (at least in this course)
-\end{itemize}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\mode<presentation>{
-\begin{frame}[c]
-\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$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\bigskip
-
-A CFG is \alert{left-recursive} if it has a nonterminal \bl{$E$} such
-that \bl{$E \rightarrow^+ E\cdot \ldots$}
-
-\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 CFG 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}Dangling Else\end{tabular}}
-
-Another ambiguous grammar:\bigskip
-
-\begin{center}
-\bl{\begin{tabular}{lcl}
-$E$ & $\rightarrow$ &  if $E$ then $E$\\
- & $|$ &  if $E$ then $E$ else $E$ \\
- & $|$ &  id 
-\end{tabular}}
-\end{center}\bigskip
-
-\bl{\texttt{if a then if x then y else c}}
-
-\end{frame}}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 
-
-\end{document}
-
-%%% Local Variables:  
-%%% mode: latex
-%%% TeX-master: t
-%%% End: 
-




