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\section*{Homework 7}

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\item Consider the following grammar 

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\begin{tabular}{l}

$S \rightarrow N\cdot P$\\

$P \rightarrow V\cdot N$\\

$N \rightarrow N\cdot N$\\

$N \rightarrow A \cdot N$\\

$N \rightarrow \texttt{student} \;|\; \texttt{trainer} \;|\; \texttt{team} \;|\; \texttt{trains}$\\

$V \rightarrow \texttt{trains} \;|\; \texttt{team}$\\

$A \rightarrow \texttt{The} \;|\; \texttt{the}$\\

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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:

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\texttt{The trainer trains the student team}

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\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:

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

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