--- a/coursework/cw01.tex Tue Jan 05 01:46:41 2016 +0000
+++ b/coursework/cw01.tex Tue Jan 12 02:18:58 2016 +0000
@@ -12,17 +12,16 @@
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. However, the coursework will \emph{only} be judged
-according to the answers. You can submit your answers in a
-txt-file or pdf.
+be awarded. You can submit your answers in a txt-file or pdf.
\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, which you can use.\bigskip
+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 use.\bigskip
\subsubsection*{Tasks}
@@ -48,9 +47,9 @@
\end{tabular}
\end{center}
-\noindent
-In the case of $r^{\{n,m\}}$ we have the convention that $0 \le n \le m$.
-The meaning of these regular expressions is
+\noindent In the case of $r^{\{n,m\}}$ we have 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}
@@ -62,49 +61,51 @@
\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 \pcode{char})).
-So $\sim{}r$ means `all the strings that $r$
-cannot match'.
+\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 \pcode{char}). So $\sim{}r$
+means `all the strings that $r$ cannot match'.
-Be careful that your implementation of $nullable$ and $der$ satisfies
-for every $r$ the following two properties (see also Question 2):
+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 $nullable(r)$ if and only if $[]\in L(r)$
-\item $L(der\,c\,r)) = Der\,c\,(L(r))$
+\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
+\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 (unmarked)}
-What is your King's email address (you will need it in Question 3)?
+What is your King's email address (you will need it in
+Question 3)?
\subsection*{Question 2 (marked with 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:
+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@ {}}
-$nullable([c_1 c_2 \ldots c_n])$ & $\dn$ & $?$\\
-$nullable(r^+)$ & $\dn$ & $?$\\
-$nullable(r^?)$ & $\dn$ & $?$\\
-$nullable(r^{\{n,m\}})$ & $\dn$ & $?$\\
-$nullable(\sim{}r)$ & $\dn$ & $?$\medskip\\
+$\textit{nullable}([c_1 c_2 \ldots c_n])$ & $\dn$ & $?$\\
+$\textit{nullable}(r^+)$ & $\dn$ & $?$\\
+$\textit{nullable}(r^?)$ & $\dn$ & $?$\\
+$\textit{nullable}(r^{\{n,m\}})$ & $\dn$ & $?$\\
+$\textit{nullable}(\sim{}r)$ & $\dn$ & $?$\medskip\\
$der\, c\, ([c_1 c_2 \ldots c_n])$ & $\dn$ & $?$\\
$der\, c\, (r^+)$ & $\dn$ & $?$\\
$der\, c\, (r^?)$ & $\dn$ & $?$\\
@@ -117,7 +118,7 @@
Remember your definitions have to satisfy the two properties
\begin{itemize}
-\item $nullable(r)$ if and only if $[]\in L(r)$
+\item $\textit{nullable}(r)$ if and only if $[]\in L(r)$
\item $L(der\,c\,r)) = Der\,c\,(L(r))$
\end{itemize}
@@ -129,11 +130,10 @@
([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, but at least apply the following six simplification
-rules:
+\noindent and calculate the derivative according to your email
+address. When calculating the derivative, simplify all regular
+expressions as much as possible, but at least apply the
+following six simplification rules:
\begin{center}
\begin{tabular}{l@{\hspace{2mm}}c@{\hspace{2mm}}ll}
@@ -149,8 +149,10 @@
\noindent
Write down your simplified derivative in the ``mathematicical''
-notation using parentheses where necessary.
-
+notation using parentheses where necessary. That means you should
+use the more readable infix notation $+$, $\cdot$ and $^*$,
+instead of code.
+
\subsection*{Question 4 (marked with 1\%)}
Suppose \textit{[a-z]} stands for the range regular expression