GATE | GATE IT 2006 | Question 80

Let L be a regular language. Consider the constructions on L below:
I. repeat (L) = {ww | w ∊ L}
II. prefix (L) = {u | ∃v : uv ∊ L}
III. suffix (L) = {v | ∃u : uv ∊ L}
IV. half (L) = {u | ∃v : | v | = | u | and uv ∊ L}
Which of the constructions could lead to a non-regular language?
(A) Both I and IV
(B) Only I
(C) Only IV
(D) Both II and III

Answer: (B)


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