A language L satisfies the Pumping Lemma for regular languages, and also the pumping Lemma for context-free languages. Which of the following statements about L is TRUE?

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Solution

If L is regular $\Rightarrow$ L satisfies the pumping lemma for regular languages.

If L is CFL $\Rightarrow$ L satisfies the pumping lemma for CFLs.

By satisfying pumping lemma, we can never say that a language is regular or CFL. It can only be used to prove that a certain language is not regular or not CFL in case the language violates the corresponding pumping lemma.

So, both regular and non-regualr languages can satisfy pumping lemma for regular language.

Similarly, both CFL's and non-CFLs can satisfy pumping lemma for CFL's

So satisfying pumping lemma doesn't prove anything about the type of language.

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