CODEWITHSUNDEEP
regexcomplement
sushi
sushi

Reputation: 41

find complement of regular expression

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?

Upvotes: 4

Views: 21615

Answers (2)

arun sharma
arun sharma

Reputation: 1

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)

Upvotes: 0

nhahtdh
nhahtdh

Reputation: 56809

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)*:

Formula 1

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).

Upvotes: 6

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