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Module 1: Introduction & Regular Languages

20222m

Let w=xyzw = xyz, yy is the middle portion and ∣y∣>0|y| > 0. Repeating yy zero or more times before checking membership in LL is known as:

(i) Generating
(ii) Pumping
(iii) Producing
(iv) None of the above

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Answer

Correct Option: (ii) Pumping

Explanation

Pumping Lemma concept: For regular/CFL languages, any long string w=xyzw = xyz (with ∣y∣>0|y|>0, ∣xy∣≤p|xy|\le p) can be pumped: xyiz∈Lxy^i z \in L for all i≥0i \ge 0 (repeating yy zero, one, or more times).

  • Pumping = repeating the middle portion yy zero or more times and checking membership.
  • Generating is general derivation.
  • Producing is vague.

The lemma is used to prove non-regularity/non-CFL by contradiction.

Final Answer

Repeating yy is Pumping → Option (ii).

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