\documentclass{article}\usepackage{charter}\usepackage{hyperref}\usepackage{amssymb}\begin{document}\section*{Homework 1}\begin{enumerate}\item {\bf (Optional)} If you want to run the code presented in the lectures, install the Scala programming language available (for free) from\begin{center}\url{http://www.scala-lang.org}\end{center}\item {\bf (Optional)} Have a look at the crawler programs. Can you find a usage for them in your daily programming life?\item In the context of the AFL-course, what is meant by the term \emph{language}?\item Give the definition for regular expressions. What is the meaning of a regular expression?\item Assume the concatenation operation of two strings is written as $s_1 @ s_2$. Define the operation of \emph{concatenating} two sets of strings.\item How is the power of a language defined? (Hint: There are two rules, one for $\_\!\_^0$ andone for $\_\!\_^{n+1}$.)\item Given the regular expressions $r_1 = \epsilon$ and $r_2 = \varnothing$ and $r_3 = a$.How many strings can the regular expressions $r_1^*$, $r_2^*$ and $r_3^*$ each match?\end{enumerate}\end{document}%%% Local Variables: %%% mode: latex%%% TeX-master: t%%% End: