Which of the following is TRUE about the Pumping Lemma for regular language?

The correct answer is It applies to all regular languages.

Key Points

• The Pumping Lemma is a property that applies to all regular languages, and it is used to prove whether a language is not regular.
  • If a language is regular, there exists some length (p) such that any string longer than p can be divided into three parts, xyz, satisfying certain conditions.
  • The conditions are: for the string xyz, the length of xy is at most p, y is not an empty string, and the string xy^iz (i ≥ 0) is still in the language.
  • The Pumping Lemma helps in identifying strings that cannot be pumped, thereby proving that the language is not regular.

Additional Information

• The Pumping Lemma does not apply to finite languages, as there is no need to pump strings in such cases.
• While the Pumping Lemma provides a necessary condition for regularity, it is not a sufficient condition; that is, some non-regular languages may satisfy the lemma.
• The lemma is a fundamental concept in the theory of computation and automata theory, helping in understanding the limitations of regular languages.
• It is an essential tool in formal language theory for distinguishing between regular and non-regular languages.