consisting of numbers, left-parenthesis $($, right-parenthesis $)$,

  identifiers and the operations $+$, $-$ and $*$. Can the following

  strings in this language be lexed?

  \begin{itemize}

  \end{itemize}

  In case they can, can you give the corresponding token

  sequences.

  string $s$. Given the following \emph{reversing} function on regular

  expressions

  \begin{center}

    \begin{tabular}{r@{\hspace{1mm}}c@{\hspace{1mm}}l}

      $rev(\varnothing)$   & $\dn$ & $\varnothing$\\

      $rev(\epsilon)$         & $\dn$ & $\epsilon$\\

      $rev(c)$                      & $\dn$ & $c$\\

      $rev(r_1 + r_2)$        & $\dn$ & $rev(r_1) + rev(r_2)$\\

      $rev(r_1 \cdot r_2)$  & $\dn$ & $rev(r_2) \cdot rev(r_1)$\\

      $rev(r^*)$                   & $\dn$ & $rev(r)^*$\\

    \end{tabular}

  \end{center}

  and the set

  \begin{center}

    $Rev\,A \dn \{s^{-1} \;|\; s \in A\}$

  \end{center}

  prove whether

  \begin{center}

    $L(rev(r)) = Rev (L(r))$

  \end{center}

  holds.

\item Assume the delimiters for comments are \texttt{$\slash$*} and

  \texttt{*$\slash$}.  Give a regular expression that can recognise

  comments of the form

  \begin{center}

    \texttt{$\slash$*~\ldots{}~*$\slash$} 

  \end{center}

  where the three dots stand for arbitrary characters, but not comment delimiters.

  (Hint: You can assume you are already given a regular expression written \texttt{ALL},

  that can recognise any character, and a regular expression \texttt{NOT} that recognises

  the complement of a regular expression.)