Cheap and Secure Web Hosting Provider : See Now

# [Solved]: what is language of repeat(L) = {ww | w ∊ L}?

, ,
Problem Detail:

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

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 .

#### Answered By : Ran G.

$repeat(\cdot)$ 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:

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

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

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