In the author means that X possibly doesn't do Y, and possibly does do Y, then I'd say just drop the "not". "X may do Y".
I'd use these:
X shall Y: X always does Y.
X shall not Y: X never does Y.
X should Y: it is expected that X will do Y, but it might not often enough that this case needs to be handled (as opposed to an "X shall Y" not doing Y which would be considered to total failure of the system).
X should not Y: it is expected that X will not do Y, but if it does you should handle it.
X may Y: both X does Y and X does not do Y are OK.