Question: Let L [ 0 ] be defined formally as { x 1 0 x 2 . . . 0 xn | xi in Sigma

Let L[0] be defined formally as {x10x2...0xn|xi in \Sigma , x1...xn in L}. In other words, strings of L[0] are formed by taking a string from L and inserting a 0 between each character of the word, so that if L ={11,1010}, then L[0]={101,1000100}. Prove that if L is regular, so is L[0].

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