Yeah their work is very cool! The two tasks are a bit different however. Their system is for the task of generating regular expressions given a set of positive and negative examples of what the regex should match. It uses genetic algorithms and other techniques to optimize and search for a regex that fits all the given examples.

In our case, we have no examples to test against, only a natural language (English) description of what the user wants the regex to do. This is an inference problem more than a search problem as we've got one shot to give our best guess without any tests to check against and modify our answer.