In Pumping Lemma for regular languages, to say a language is satisfying…

2022

In Pumping Lemma for regular languages, to say a language is satisfying pumping lemma, what is the minimum length of ' y ' if you consider the string as ' xyz '.

  1. A.

    n

  2. B.

    2

  3. C.

    1

  4. D.

    0

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Correct answer: C

Answer: The minimum length of y is 1.

  • Pumping lemma statement: For any regular language there is a pumping length n such that any string s in the language with |s| ≥ n can be split as s = xyz with |xy| ≤ n and |y| ≥ 1.

  • Implication for the length of y: The condition |y| ≥ 1 means y must contain at least one symbol, so its minimum possible length is 1.

  • Common confusion: Do not confuse the pumping length n (which bounds |xy|) with |y|. The bound on |xy| restricts where y appears in the prefix, but it does not force y to have length n.

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