in Theory of Computation
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Let $L$ be a regular language. Consider the constructions on $L$ below:

  1. repeat $(L) = \{ww \mid  w \in  L\}$
  2. prefix $(L) = \{u \mid ∃v : uv \in L\}$
  3. suffix $(L) = \{v \mid  ∃u : uv \in L\}$
  4. half $(L) = \{u \mid ∃v : | v | = | u | \text{ and } uv \in L\}$

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

  1. Both I and IV
  2. Only I
  3. Only IV
  4. Both II and III
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