\documentclass{article}\usepackage{charter}\usepackage{hyperref}\usepackage{amssymb}\usepackage{amsmath}\newcommand{\dn}{\stackrel{\mbox{\scriptsize def}}{=}}% for definitions\begin{document}\section*{Homework 4}\begin{enumerate}\item Give an automaton that can recognise the language $L(a^*\cdot b\cdot b^*\cdot(a\cdot a^*\cdot b\cdot b^*)^*)$.\item Assume that $s^{-1}$ stands for the operation of reversing astring $s$. Given the following \emph{reversing} function on regular expressionsand the set\begin{center}$Rev\,A \dn \{s^{-1} \;|\; s \in A\}$\end{center}prove that\begin{center}$L(rev(r)) = Rev (L(r))$\end{center}holds.\item Palindromes\item (Optional) The tokenizer in \texttt{regexp3.scala} takes asargument a string and a list of rules. The result is a list of tokens. Improve this tokenizer so that it filters out all comments and whitespace from the result.\item (Optional) Modify the tokenizer in \texttt{regexp2.scala} so that itimplements the \texttt{findAll} function. This function takes a regularexpressions and a string, and returns all substrings in this string that match the regular expression.\end{enumerate}\end{document}%%% Local Variables: %%% mode: latex%%% TeX-master: t%%% End: