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     8 \section*{Homework 1}

     9 

    10 \begin{enumerate}

    11 \item {\bf (Optional)} If you want to run the code presented 

    12 in the lectures, install the 

    13 Scala programming language available (for free) from

    14 \begin{center}

    15 \url{http://www.scala-lang.org}

    16 \end{center}

    17 

    18 \item {\bf (Optional)} Have a look at the crawler programs. 

    19 Can you find a usage for them in your daily programming life?

    20 

    21 \item In the context of the AFL-course, what is meant by the term \emph{language}?

    22 

    23 \item Give the definition for regular expressions. What is the meaning of a 

    24 regular expression?

    25 

    26 \item Assume the concatenation operation of two strings is written as $s_1 @ s_2$. 

    27 Define the operation  of \emph{concatenating} two sets of strings.

    28 

    29 \item How is the power of a language defined? (Hint: There are two rules, one for $\_\!\_^0$ and

    30 one for $\_\!\_^{n+1}$.)

    31 

    32 \item Given the regular expressions $r_1 = \epsilon$ and $r_2 = \varnothing$ and $r_3 = a$.

    33 How many strings can the regular expressions $r_1^*$, $r_2^*$ and $r_3^*$ each match?

    34 

    35 \end{enumerate}

    36 

    37 \end{document}

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