A language L satisfies the Pumping Lemma for regular languages, and also the…
2005
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?
- A.
L is necessarily a regular language.
- B.
L is necessarily a context-free language, but not necessarily a regular language
- C.
L is necessarily a non-regular language
- D.
None of the above
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Correct answer: D
The Pumping Lemma for regular languages is a necessary condition for regularity, but not sufficient. Similarly, the Pumping Lemma for context-free languages is necessary for context-freeness but not sufficient. A language satisfying both lemmas does not guarantee it is regular or context-free, as there are non-regular and non-context-free languages that may satisfy the lemmas. Therefore, none of the statements A, B, or C must be true, making D correct.