There is an open problem in formal languages known as the Separating Problem; which is briefly stated as given two distinct strings of length $n$, how large of a DFA is required to "separate" them, meaning accept one string but reject the other.
These all discuss the problem of separating two distinct strings. I am wondering if there been any work done in the area of separating lists of strings, meaning given two lists of strings, $A$ and $B$, what size DFA is required to accept every string in $A$ and reject every string in $B$. This problem is equivalent to regex golf.
There are some basic questions that I have been working on such as if one of the lists is of size $1$ or if all the strings are of different lengths.
I have been searching around but haven't found any papers that deal with this type of problem. Has there been any research done in this area?
Thanks in advance.