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