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The pumping lemma for regular languages is used to prove that a language

  • A.is regular by constructing some automaton that accepts all of it
  • B.is context free by exhibiting a suitable grammar for it
  • C.is accepted by some deterministic pushdown automaton
  • D.is not regular by exhibiting a string that cannot be pumped

Answer: D

Correct answer: is not regular by exhibiting a string that cannot be pumped

The lemma states a property that every regular language must have, so it is used contrapositively: choose a string in the language long enough that the lemma would apply, show that no way of pumping it stays inside the language, and conclude that the language is not regular. It can never be used to prove that a language is regular.

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