
diff -r b17eff695c7f -r 2e9134d25a2b slides/slides07.tex
--- a/slides/slides07.tex	Mon Nov 11 13:48:34 2013 +0000
+++ b/slides/slides07.tex	Mon Nov 11 15:26:20 2013 +0000
@@ -76,152 +76,6 @@
 \newcommand{\bl}[1]{\textcolor{blue}{#1}}       
 \newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions
 
-
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 \begin{document}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -262,18 +116,13 @@
 \item a start symbol (which must be a nonterminal)
 \item a set of rules
 \begin{center}
-\bl{$A \rightarrow \text{rhs}$}
+\bl{$A \rightarrow \text{rhs}_1 | \text{rhs}_2 | \ldots$}
 \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}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
 
@@ -281,17 +130,21 @@
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}A CFG Derivation\end{tabular}}
+\frametitle{\begin{tabular}{c}Hierarchie of Languages\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}
+Recall that languages are sets of strings.
 
 \begin{center}
-\bl{$S \rightarrow \ldots \rightarrow \ldots  \rightarrow \ldots  \rightarrow \ldots $}
+\begin{tikzpicture}
+[rect/.style={draw=black!50, top color=white,bottom color=black!20, rectangle, very thick, rounded corners}]
+
+\draw (0,0) node [rect, text depth=39mm, text width=68mm] {all languages};
+\draw (0,-0.4) node [rect, text depth=28.5mm, text width=64mm] {decidable languages};
+\draw (0,-0.85) node [rect, text depth=17mm] {context sensitive languages};
+\draw (0,-1.14) node [rect, text depth=9mm, text width=50mm] {context-free languages};
+\draw (0,-1.4) node [rect] {regular languages};
+\end{tikzpicture}
+
 \end{center}
 
 \end{frame}}
@@ -299,45 +152,87 @@
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
+\begin{frame}[t]
+\frametitle{\begin{tabular}{c}Numbers\end{tabular}}
+
+A grammar for numbers:
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ &  $N \cdot N \;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
+\end{tabular}}
+\end{center}
+
+Unfortunately left-recursive (and ambiguous).\medskip\\
+A problem for \alert{recursive descent parsers} (e.g.~parser combinators).
+\bigskip\pause
+
+A non-left-recursive grammar for numbers
+
+\begin{center}
+\bl{\begin{tabular}{lcl}
+$N$ & $\rightarrow$ &  $0 \cdot N \;|\;1 \cdot N \;|\ldots\;|\; 0 \;|\; 1 \;|\; \ldots \;|\; 9$\\
+\end{tabular}}
+\end{center}
+
+
+\end{frame}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Language of a CFG\end{tabular}}
+\frametitle{\begin{tabular}{c}Chomsky Normal Form\end{tabular}}
 
-Let \bl{$G$} be a context-free grammar with start symbol \bl{$S$}. 
-Then the language \bl{$L(G)$} is:
+All rules must be of the form
 
 \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
+\bl{$A \rightarrow a$}
+\end{center}
+
+or
 
-\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}
+\begin{center}
+\bl{$A \rightarrow B\cdot C$}
+\end{center}
+
+
 
 \end{frame}}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \mode<presentation>{
 \begin{frame}[c]
-\frametitle{\begin{tabular}{c}Arithmetic Expressions\end{tabular}}
+\frametitle{\begin{tabular}{c}CYK Algorithm\end{tabular}}
+
 
 \begin{center}
-\bl{\begin{tabular}{lcl}
-$E$ & $\rightarrow$ &  $num\_token$ \\
-$E$ & $\rightarrow$ &  $E \cdot + \cdot E$ \\
-$E$ & $\rightarrow$ &  $E \cdot - \cdot E$ \\
-$E$ & $\rightarrow$ &  $E \cdot * \cdot E$ \\
-$E$ & $\rightarrow$ &  $( \cdot E \cdot )$ 
+\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}\pause\bigskip
+\end{center}
 
-A CFG is \alert{left-recursive} if it has a nonterminal \bl{$E$} such
-that \bl{$E \rightarrow^+ E\cdot \ldots$}
+\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}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -427,6 +322,26 @@
 \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}}
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   
+
+
 \end{document}
 
 %%% Local Variables:  




