76 because in general the set of strings $L$ returns is infinite

    76 because in general the set of strings $L$ returns is infinite

    77 (recall what $L(a^*)$ is). In such cases there is no way we

    77 (recall what $L(a^*)$ is). In such cases there is no way we

    78 can implement an exhaustive test for whether a string is

    78 can implement an exhaustive test for whether a string is

    79 member of this set or not. In contrast our matching algorithm

    79 member of this set or not. In contrast our matching algorithm

    80 will operate on the regular expression $r$ and string $s$,

    80 will operate on the regular expression $r$ and string $s$,

    82 algorithm, however, let us have a closer look at what it means

    82 algorithm, however, let us have a closer look at what it means

    83 when two regular expressions are equivalent.

    83 when two regular expressions are equivalent.

    84 

    84 

    85 \subsection*{Regular Expression Equivalences}

    85 \subsection*{Regular Expression Equivalences}

    86 

    86 

   581 \addplot[black,mark=square*,mark options={fill=white}] table {re3.data};

   581 \addplot[black,mark=square*,mark options={fill=white}] table {re3.data};

   582 \end{axis}

   582 \end{axis}

   583 \end{tikzpicture}

   583 \end{tikzpicture}

   584 \end{center}

   584 \end{center}

   585 

   585 

   586 \end{document}

   588 \end{document}

   587 

   589 

   588 

   590 

   589 

   591 

   590 

   592