# 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.

## closed as unclear what you're asking by Yuval Filmus, David Richerby, Evil, vonbrand, codyAug 30 '15 at 3:50

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the 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

## 1 Answer

$repeat(\cdot)$ 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 $repeat(L)$.

A Few examples:

$L=\{ 0,00, 11\}$ => $repeat(L) = \{ 00,0000,1111\}$

$L=\{ \}$ => $repeat(L) = \{ \}$

$L=\Sigma^*=\{\epsilon,0,1,00,01,10,11,...\}$ => $repeat(L)= \{\epsilon, 00,11,0000,0101,1010,1111,...\}$