# What is language of repeat(L) = {ww | w ∊ L}? [closed]

What is language of repeat(L) = {ww | w ∊ L} ?

### My try:

I know it {ww | w ∊ (a,b)*} is context sensitive language. Here , what is meant by "repeat(L)" ? Can you explain it ? It is not a homework question.

• The notation "repeat(L)" is defined in your question. – Yuval Filmus Aug 29 '15 at 9:55
• It's hard to tell from your question what your particular confusion is. I suggest that you edit the question to explain what you don't understand. You already wrote a definition of repeat(L); what about it is confusing? Do you know what the notation means? What are your thoughts -- if you had to guess what it means, what would your guess be? What possible meanings have you considered? What self-study have you done? You can find more tips about how to ask a good question here: cs.stackexchange.com/help/how-to-ask – D.W. Aug 30 '15 at 4:03

$$repeat(\cdot)$$ is an operator on languages. It takes as an input a language $$L$$, and outputs a language defined by $$\{ xx \mid x \in L\}$$. That is, for any word $$x\in L$$ the string $$xx$$ will be in the output language $$repeat(L)$$.
$$L=\{ 0,00, 11\}$$ => $$repeat(L) = \{ 00,0000,1111\}$$
$$L=\{ \}$$ => $$repeat(L) = \{ \}$$
$$L=\Sigma^*=\{\epsilon,0,1,00,01,10,11,...\}$$ => $$repeat(L)= \{\epsilon, 00,11,0000,0101,1010,1111,...\}$$