It is well known that "regex" with back-reference is not a regular expression anymore.
For instance, (.*)\1 matches any string repeated twice.
However, is it possible to construct a DFA for regex with lookaround?
I found this question and particularly this answer, which says
Look-ahead and look-behind are nothing special in the world of finite automata as we only match whole inputs here. Therefore, the special semantic of "just check but don't consume" is meaningless; you just concatenate and/or intersect checking and consuming expressions and use the resulting automata.
(emphasis mine)
However, I'm not quite sure how to intersect the checking and matching automata.
For simple cases such as foo(?=bar), I can just concatenate them (foobar).
But this won't work for more complex cases such as foo(?=bar)(?=baz):
since lookahead will not consume the input,
what follows foo must match both bar and baz.
This answer suggests using Alternating Finite Automaton,
but after reading through the tremendously unhelpful Wikipedia page,
I am totally confused how this can help turn lookarounds into plain old DFA.
