Regular expression matching is a classical and well-studied problem.
Prior work applies DFA and Thompson NFA methods for the construction
of the matching automata. We propose the novel use of derivatives and
partial derivatives for regular expression matching.
We show how to obtain algorithms for various
matching policies such as POSIX and greedy left-to-right.
Our benchmarking results show that the run-time performance is promising
and that our approach can be applied in practice.
This is a topic, Kenny and I have pursued for quite a while and we have finally
managed to write up the ideas.
Here's the link to the paper
The implementation is on hackage. See regex-pderiv
[Edit: regex-pderiv replaces xhaskell-library]