Turning evil regexes harmless

We explore the relationship between ambiguity in automata and regular expressions on the one hand, and the matching time of backtracking regular expression matchers on the other. We focus in particular on the extreme cases where we have either an exponential amount of ambiguity or no ambiguity at all. We also investigate techniques to reduce or remove ambiguity from regular expressions, which can then be used to transform regular expressions which might be exploited by using algorithmic complexity, into harmless equivalent expressions.