How do Deterministic Finite Automata (DFA) work and why are they effective for regex matching?

DFAs work by accepting input one unit at a time and determining at each step whether to continue evaluation. This step-by-step processing makes state machines particularly efficient at identifying negative cases, quickly determining when strings don't match a pattern. Benchmarking shows that while regex implementations take about twice as long as hashmap-based solutions, they're still impressively fast given their complexity. This efficiency is particularly valuable in Cloudflare's environment where typically only one or two headers per request need to be checked, making DFA-based regex matching an effective approach for processing high volumes of requests.