almost every regex engine today descends from one of two approaches: Thompson’s NFA construction (1968) or backtracking (1994). Thompson-style engines (grep, RE2, Rust’s regex) give you linear-time guarantees but only support the “standard” fragment - | and *. backtracking engines (the rest, 95% chance the one you’re using) give you a mix of advanced features like backreferences, lookarounds.., but are unreliable, and can blow up to exponential time on adversarial inputs, which is a real security concern known as ReDoS. to be more precise, this exponential behavior is not the only problem with backtracking engines - they also handle the OR (|) operator much slower, but let’s try to start with the big picture.
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O(1) / O(log n) / O(n) hierarchy. Operations fall into three tiers: O(1) single-pass。关于这个话题，PDF资料提供了深入分析