
diff -r c1e6123d02f4 -r aae256985251 cws/cw01.tex
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/cws/cw01.tex	Thu Nov 03 00:53:53 2016 +0000
@@ -0,0 +1,217 @@
+\documentclass{article}
+\usepackage{style}
+%%\usepackage{../langs}
+
+\begin{document}
+
+\section*{Coursework 1 (Strand 1)}
+
+This coursework is worth 4\% and is due on 25 October at
+16:00. You are asked to implement a regular expression matcher
+and submit a document containing the answers for the questions
+below. You can do the implementation in any programming
+language you like, but you need to submit the source code with
+which you answered the questions, otherwise a mark of 0\% will
+be awarded. You can submit your answers in a txt-file or pdf.
+Code send as code.
+
+
+
+\subsubsection*{Disclaimer}
+
+It should be understood that the work you submit represents
+your own effort. You have not copied from anyone else. An
+exception is the Scala code I showed during the lectures or
+uploaded to KEATS, which you can freely use.\bigskip
+
+
+\subsubsection*{Task}
+
+The task is to implement a regular expression matcher based on
+derivatives of regular expressions. The implementation should
+be able to deal with the usual (basic) regular expressions
+
+\[
+\ZERO,\; \ONE,\; c,\; r_1 + r_2,\; r_1 \cdot r_2,\; r^*
+\]
+
+\noindent
+but also with the following extended regular expressions:
+
+\begin{center}
+\begin{tabular}{ll}
+$[c_1 c_2 \ldots c_n]$ & a range of characters\\
+$r^+$ & one or more times $r$\\
+$r^?$ & optional $r$\\
+$r^{\{n,m\}}$ & at least $n$-times $r$ but no more than $m$-times\\
+$\sim{}r$ & not-regular expression of $r$\\
+\end{tabular}
+\end{center}
+
+\noindent In the case of $r^{\{n,m\}}$ you can assume the
+convention that $0 \le n \le m$. The meanings of the extended
+regular expressions are
+
+\begin{center}
+\begin{tabular}{r@{\hspace{2mm}}c@{\hspace{2mm}}l}
+$L([c_1 c_2 \ldots c_n])$ & $\dn$ & $\{[c_1], [c_2], \ldots, [c_n]\}$\\ 
+$L(r^+)$                  & $\dn$ & $\bigcup_{1\le i}. L(r)^i$\\
+$L(r^?)$                  & $\dn$ & $L(r) \cup \{[]\}$\\
+$L(r^{\{n,m\}})$           & $\dn$ & $\bigcup_{n\le i \le m}. L(r)^i$\\
+$L(\sim{}r)$              & $\dn$ & $\Sigma^* - L(r)$
+\end{tabular}
+\end{center}
+
+\noindent whereby in the last clause the set $\Sigma^*$ stands
+for the set of \emph{all} strings over the alphabet $\Sigma$
+(in the implementation the alphabet can be just what is
+represented by, say, the type \texttt{Char}). So $\sim{}r$
+means `all the strings that $r$ cannot match'. 
+
+Be careful that your implementation of \textit{nullable} and
+\textit{der} satisfies for every $r$ the following two
+properties (see also Question 2):
+
+\begin{itemize}
+\item $\textit{nullable}(r)$ if and only if $[]\in L(r)$
+\item $L(der\,c\,r) = Der\,c\,(L(r))$
+\end{itemize}
+
+\noindent {\bf Important!} Your implementation should have
+explicit cases for the basic regular expressions, but also
+explicit cases for the extended regular expressions. That
+means do not treat the extended regular expressions by just
+translating them into the basic ones. See also Question 2,
+where you are asked to explicitly give the rules for
+\textit{nullable} and \textit{der} for the extended regular
+expressions.
+
+
+\subsection*{Question 1}
+
+What is your King's email address (you will need it in
+Question 3)?
+
+\subsection*{Question 2}
+
+This question does not require any implementation. From the
+lectures you have seen the definitions for the functions
+\textit{nullable} and \textit{der} for the basic regular
+expressions. Give the rules for the extended regular
+expressions:
+
+\begin{center}
+\begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}
+$\textit{nullable}([c_1 c_2 \ldots c_n])$  & $\dn$ & $?$\\
+$\textit{nullable}(r^+)$                   & $\dn$ & $?$\\
+$\textit{nullable}(r^?)$                   & $\dn$ & $?$\\
+$\textit{nullable}(r^{\{n,m\}})$            & $\dn$ & $?$\\
+$\textit{nullable}(\sim{}r)$               & $\dn$ & $?$\medskip\\
+$der\, c\, ([c_1 c_2 \ldots c_n])$  & $\dn$ & $?$\\
+$der\, c\, (r^+)$                   & $\dn$ & $?$\\
+$der\, c\, (r^?)$                   & $\dn$ & $?$\\
+$der\, c\, (r^{\{n,m\}})$            & $\dn$ & $?$\\
+$der\, c\, (\sim{}r)$               & $\dn$ & $?$\\
+\end{tabular}
+\end{center}
+
+\noindent
+Remember your definitions have to satisfy the two properties
+
+\begin{itemize}
+\item $\textit{nullable}(r)$ if and only if $[]\in L(r)$
+\item $L(der\,c\,r)) = Der\,c\,(L(r))$
+\end{itemize}
+
+\subsection*{Question 3}
+
+Implement the following regular expression for email addresses
+
+\[
+([a\mbox{-}z0\mbox{-}9\_\!\_\,.-]^+)\cdot @\cdot ([a\mbox{-}z0\mbox{-}9\,.-]^+)\cdot .\cdot ([a\mbox{-}z\,.]^{\{2,6\}})
+\]
+
+\noindent and calculate the derivative according to your email
+address. When calculating the derivative, simplify all regular
+expressions as much as possible by applying the
+following 7 simplification rules:
+
+\begin{center}
+\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}ll}
+$r \cdot \ZERO$ & $\mapsto$ & $\ZERO$\\ 
+$\ZERO \cdot r$ & $\mapsto$ & $\ZERO$\\ 
+$r \cdot \ONE$ & $\mapsto$ & $r$\\ 
+$\ONE \cdot r$ & $\mapsto$ & $r$\\ 
+$r + \ZERO$ & $\mapsto$ & $r$\\ 
+$\ZERO + r$ & $\mapsto$ & $r$\\ 
+$r + r$ & $\mapsto$ & $r$\\ 
+\end{tabular}
+\end{center}
+
+\noindent Write down your simplified derivative in a readable
+notation using parentheses where necessary. That means you
+should use the infix notation $+$, $\cdot$, $^*$ and so on,
+instead of code.
+ 
+\subsection*{Question 4}
+
+Suppose \textit{[a-z]} stands for the range regular expression
+$[a,b,c,\ldots,z]$.  Consider the regular expression $/ \cdot * \cdot
+(\sim{}([a\mbox{-}z]^* \cdot * \cdot / \cdot [a\mbox{-}z]^*)) \cdot *
+\cdot /$ and decide wether the following four strings are matched by
+this regular expression. Answer yes or no.
+
+\begin{enumerate}
+\item \texttt{"/**/"}
+\item \texttt{"/*foobar*/"}
+\item \texttt{"/*test*/test*/"}
+\item \texttt{"/*test/*test*/"}
+\end{enumerate}
+
+\noindent
+Also test your regular expression matcher with the regular
+expression $a^{\{3,5\}}$ and the strings
+
+\begin{enumerate}
+\setcounter{enumi}{4}
+\item \texttt{aa}
+\item \texttt{aaa}
+\item \texttt{aaaaa}
+\item \texttt{aaaaaa}
+\end{enumerate}
+
+\noindent
+Does your matcher produce the expected results?
+
+\subsection*{Question 5}
+
+Let $r_1$ be the regular expression $a\cdot a\cdot a$ and $r_2$ be
+$(a^{\{19,19\}}) \cdot (a^?)$.  Decide whether the following three
+strings consisting of $a$s only can be matched by $(r_1^+)^+$.
+Similarly test them with $(r_2^+)^+$. Again answer in all six cases
+with yes or no. \medskip
+
+\noindent
+These are strings are meant to be entirely made up of $a$s. Be careful
+when copy-and-pasting the strings so as to not forgetting any $a$ and
+to not introducing any other character.
+
+\begin{enumerate}
+\item \texttt{"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"}
+\item \texttt{"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ 
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ 
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"}
+\item \texttt{"aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ 
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa\\ 
+aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa"}
+\end{enumerate}
+
+
+\end{document}
+
+%%% Local Variables: 
+%%% mode: latex
+%%% TeX-master: t
+%%% End: 




