Not sure about the "math" language of that but ill try to explain my question:
Assume we have two regexes A, B. I say Regex A is a "full subset" of B if every input that matches A will also matches B.
Small example, A= a.* B=.*
Every input in A will also match in B. So A ⊆ B
Now my question is, how this relates to the complements groups? Say the complements of A and B are ~A and ~B. Does ~A ⊆ ~B? what about ~A and B or A and ~B?
I mean by complement is the group that contains all the input that dont match A
And what if A is not a full subset of B? Can we say anything about the compliments?
Thanks!