Self doubt

Question

If the complement of a language L is not regular , then L may satisfy pumping lemma for regular languages.

Is this statement correct?

Answer 1

If a language does not satisfy $pumping\,lemma$ it is not $regular$, but if a language satisfies $pumping\,lemma$ then it may or may not be $regular$ and every $regular\,language$ will satisfy $pumping\,lemma$.

In the above statement, complement of langauge $L$ is not $regular$. So, $L$ is not $regular$, So, it may or may not satisfy $Pumping\,lemma$.

So, the above statement is correct.

Answer 2

Language if it does not satisfy "pumping lemma" then it is definitely not regular but if it satisfies pumping lemma it may or may not be regular.

Comments

Wrongly understood

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thnxx bro, i done mistake here

Answer 3

Pumping Lemma is a negativity test. A negativity test means that does who donot pass this test are definitely not there but those who pass may or may not be there. So For any Language if it does not satisfy "pumping lemma" then it is definitely not regular but if it satisfies pumping lemma it may or may not be regular.

Coming to the statement:If the complement of a language L is not regular , then L may satisfy pumping lemma for regular languages.

Regular languages are closed under complementation So L is not a regular lang.

As L is not regular it may or may not satisfy the pumping lemma.(as it is a negativity test) So it is true

Comments

You misunderstand the given statement

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got it.... thanks @Shaik Masthan