1232 from $v$ is not so straightforward. The point of this is that  we might

  1232 from $v$ is not so straightforward. The point of this is that  we might

  1233 be able to finally bridge the gap by proving

  1233 be able to finally bridge the gap by proving

  1234 

  1234 

  1235 \begin{center}

  1235 \begin{center}

  1236 $\textit{retrieve} \; (r^\uparrow   \backslash  s) \; v = \;\textit{retrieve} \;

  1236 $\textit{retrieve} \; (r^\uparrow   \backslash  s) \; v = \;\textit{retrieve} \;

  1238 \end{center}

  1238 \end{center}

  1239 

  1239 

  1240 \noindent

  1240 \noindent

  1241 and subsequently

  1241 and subsequently

  1242 

  1242 

  1277 deal more efficiently with back-references, which are one of the

  1277 deal more efficiently with back-references, which are one of the

  1278 reasons why regular expression engines in JavaScript, Python and Java

  1278 reasons why regular expression engines in JavaScript, Python and Java

  1279 choose to not implement the classic automata approach of transforming

  1279 choose to not implement the classic automata approach of transforming

  1280 regular expressions into NFAs and then DFAs---because we simply do not

  1280 regular expressions into NFAs and then DFAs---because we simply do not

  1281 know how such back-references can be represented by DFAs.

  1281 know how such back-references can be represented by DFAs.

  1283 

  1290 

  1284 \bibliographystyle{plain}

  1291 \bibliographystyle{plain}

  1285 \bibliography{root}

  1292 \bibliography{root}

  1286 

  1293 

  1287 

  1294