For what it's worth, the inbuilt HTML5 validation that implementw input type=email does have a regex in the spec.

https://html.spec.whatwg.org/#email-state-(type=email)

  /^[a-zA-Z0-9.!#$%&'*+\/=?^_`{|}~-]+@[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?(?:\.[a-zA-Z0-9](?:[a-zA-Z0-9-]{0,61}[a-zA-Z0-9])?)*$/

But it is true that you can implement it with a FSM(which is what firefox does). Webkit uses a regex as well I think.