of course this rabbit hole goes deeper, and we have a paper using this technique for string constraint solving that i’d love to derail this post into, but i’ll save that for another time. the main point is that symbolic derivatives are a more powerful and efficient generalization of Brzozowski’s original idea, and they form the core of the new RE# engine. fun fact: symbolic derivatives are also implemented in Z3 (the SMT solver) for its sequence theory - so in some sense we’re inching closer to having an SMT solver’s core machinery inside a regex engine.
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