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DFA construction is O(2^m) in the worst case, where m is the size of the NFA. this is widely known in academic circles, but in practice, most people think well of DFAs because they are used in tools like grep that are optimized for the common case. but if you throw a large regex at them, they will blow up in size and become unusable. DFA matching is linear O(n) where n is the size of the input, and the constant is ~3-4 assembly instructions per character - faster than anything you could write by hand.
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One of the most important problems in computer security is user authentication. Often when you visit a website, log into a server, access a resource, you (and generally, your computer) needs to convince the provider that you’re authorized to access the resource. This authorization process can take many forms. Some sites require explicit user logins, which users complete using traditional username and passwords credentials, or (increasingly) advanced alternatives like MFA and passkeys. Some sites that don’t require explicit user credentials, or allow you to register a pseudonymous account; however even these sites often ask user agents to prove something. Typically this is some kind of basic “anti-bot” check, which can be done with a combination of long-lived cookies, CAPTCHAs, or whatever the heck Cloudflare does: