107   negation and back-references.

   107   negation and back-references.

   108 \end{abstract}

   108 \end{abstract}

   109 

   109 

   110 

   110 

   111 \section{Introduction}

   111 \section{Introduction}

   113 While we believe derivatives of regular expressions, written

   113 While we believe derivatives of regular expressions, written

   114 $r\backslash s$, are a beautiful concept (in terms of ease of

   114 $r\backslash s$, are a beautiful concept (in terms of ease of

   115 implementing them in functional programming languages and in terms of

   115 implementing them in functional programming languages and in terms of

   116 reasoning about them formally), they have one major drawback: every

   116 reasoning about them formally), they have one major drawback: every

   117 derivative step can make regular expressions grow drastically in

   117 derivative step can make regular expressions grow drastically in