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\begin{document}

\section*{Handout 2}

Having specified what problem our matching algorithm, $match$, is supposed to solve, namely
for a given regular expression $r$ and string $s$ answer $true$ if and only if

\[
s \in L(r)
\]

\noindent
Clearly we cannot use the function $L$ directly in order to solve this problem, because in general
the set of strings $L$ returns is infinite (recall what $L(a^*)$ is). In such cases there is no algorithm
then can test exhaustively, whether a string is member of this set.

The algorithm we define below consists of two parts. One is the function $nullable$ which takes a
regular expression as argument and decides whether it can match the empty string. This can be easily 
defined recursively as follows:


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