问题
There's a question on my exercise sheet to find the complement of two formulas
(1) (aa|bb)*
and
(2) (a|b)(aa|bb)(a|b).
complement of both is in my opinion a* | b*, meaning only a's or only b's?
回答1:
You need to go through the usual procedure:
- Convert regex to NFA.
- Convert NFA to DFA. For simple case, it is easy to convert (by hand) from regex to DFA directly.
- Turn all non-terminal state into terminal states and vice versa.
- Convert the complementing DFA to regex. This is one detailed example of such conversion
I won't show you the result since it is exercise, but I will show you the DFA for the first formula (aa|bb)*:
From this, you can see clearly that a* or b* will not give the correct result. You will never end up in the Trap state (which becomes a terminal state in the complementing regular expression), and you may end up in state 2a/2b (which becomes non-terminal state in the complementing regular expression).
回答2:
simply (aa+bb)* will contain sample strings such as null, aa , aaaa , bb , bbbb ,aabb, bbaa and so on observe that all strings that can be formed are of even length and a and b can be any order , so complement should contain all odd length strings
((a+b)(a+b))*(a+b)
来源：https://stackoverflow.com/questions/15452353/find-complement-of-regular-expression