\documentclass{article}

\usepackage{../style}

\usepackage{../grammar}

\begin{document}

\section*{Homework 7}

\HEADER

\begin{enumerate}

\item Suppose the context-sensitive grammar

\begin{center}

\begin{tabular}{lcl}

\end{tabular}

\end{center}

where $S$ is the starting symbol of the grammar. 

Give a derivation  of the string $"\!aaabaaabb"$. 

What can you say about the number of as and bs in the

strings recognised by this grammar.

\item Consider the following grammar 

\begin{plstx}[margin=1cm]

  : \meta{S\/} ::= \meta{N\/}\cdot \meta{P\/}\\

  : \meta{P\/} ::= \meta{V\/}\cdot \meta{N\/}\\

  : \meta{N\/} ::= \meta{N\/}\cdot \meta{N\/}\\

  : \meta{N\/} ::= \meta{A\/}\cdot \meta{N\/}\\

  : \meta{N\/} ::= \texttt{student} \mid \texttt{trainer} \mid \texttt{team} \mid \texttt{trains}\\

  : \meta{V\/} ::= \texttt{trains} \mid \texttt{team}\\

  : \meta{A\/} ::= \texttt{The} \mid \texttt{the}\\

\end{plstx}

where $S$ is the start symbol and $S$, $P$, $N$, $V$ and $A$ are non-terminals.

Using the CYK-algorithm, check whether or not the following string can be parsed

by the grammar:

\begin{center}

\texttt{The trainer trains the student team}

\end{center}

\item Transform the grammar

\begin{center}

\begin{tabular}{lcl}

\end{tabular}

\end{center}

\noindent

into Chomsky normal form.

\item Consider the following grammar $G$

\begin{center}

\begin{tabular}{l}

\end{tabular}

\end{center}

where $S$ is the start symbol and $S$, $E$ and $B$ are

non-terminals.

Check each rule below and decide whether, when added to $G$,

the combined grammar is ambiguous. If yes, give a string that

has more than one parse tree.

\begin{center}

\begin{tabular}{rl}

\end{tabular}

\end{center}

%\item {\bf (Optional)} The task is to match strings where the letters are in alphabetical order---for example, 

%\texttt{abcfjz} would pass, but \texttt{acb} would not. Whitespace should be ignored---for example

%\texttt{ab c d} should pass. The point is to try to get the regular expression as short as possible!

%See:

%\begin{center}

%\url{http://callumacrae.github.com/regex-tuesday/challenge11.html}

%\end{center}

\end{enumerate}

\end{document}

%%% Local Variables: 

%%% mode: latex

%%% TeX-master: t

%%% End: