Let L be a regular language. Consider the constructions on L below: repeat (L)…

GATE · 2006 · IT

Let L be a regular language. Consider the constructions on L below:

repeat (L) = {ww | w ∊ L}

prefix (L) = {u | ∃v : uv ∊ L}

suffix (L) = {v | ∃u uv ∊ L}

half (L) = {u | ∃v : | v | = | u | and uv ∊ L}

Which of the constructions could lead to a non-regular language?

  1. A.

    Both I and IV

  2. B.

    Only I

  3. C.

    Only IV

  4. D.

    Both II and III

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