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\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 Read the handout of the first lecture and make sure you
understand the concepts of strings and languages. 

\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 Assume a set $A$ contains 4 strings and a set $B$ 7 strings, how many strings
are in $A @ B$?

\item How is the power of a language defined? (Hint: There are two rules, one for $\_\!\_^0$ and
one for $\_\!\_^{n+1}$.)


\end{enumerate}

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