I’m not very familiar with the implications of lookaheads, but your example of "abcd" =~ /^ab(?=.*foo)cd/ seems rather unproblematic to me. The engine would go looking for “foo” and thereby bump into the end of string, which means that "abcd" cannot be ruled out as a potential prefix of some match of the given pattern (which is indeed correct, because it is a prefix of, e.g., "abcdfoo"). Can you think of a case in which the algorithm gives the wrong answer?

Compare the results against "abxy" =~ /^ab(?=.*foo)cd/. The Cartesian product approach will say for both cases that "ab" =~ /^ab/ is the longest matching prefix, while checking what characters are looked at would claim the whole string is ok in both cases.

Your next example is more interesting. I agree that applying the algorithm to "ab" =~ /^abc(?<=d)/ would fail to establish that "ab" is not a prefix of any matching string. But this is an imaginary/academic problem, because the given regular expression would never occur in the real world except as an outright bug. I wonder if the problem can occur non-pathological cases (i.e., for regular expressions that can actually match things). Can you think of any example?

Well unmatchable patterns could quite reasonably arise in some situations, particularly if they are themselves generated. But I think the likely real-world problems would occur with backreferences, of the /^(something)other\1/ variety, but I can't think of a concrete example off the top of my head.

Hugo