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   146 the set of strings $L$ returns is infinite (recall what $L(a^*)$ is).

   147 the set of strings $L$ returns is infinite (recall what $L(a^*)$ is).

   147 In such cases there is no way we can implement an exhaustive test for

   148 In such cases there is no way we can implement an exhaustive test for

   148 whether a string is member of this set or not. In contrast our

   149 whether a string is member of this set or not. In contrast our

   149 matching algorithm will operate on the regular expression $r$ and

   150 matching algorithm will operate on the regular expression $r$ and

   150 string $s$, only, which are both finite objects. Before we explain 

   151 string $s$, only, which are both finite objects. Before we explain 

   152 means when two regular expressions are equivalent.

   153 means when two regular expressions are equivalent.

   153 

   154 

   154 \subsection*{Regular Expression Equivalences}

   155 \subsection*{Regular Expression Equivalences}

   155 

   156 

   156 We already defined in Handout 1 what it means for two regular

   157 We already defined in Handout 1 what it means for two regular