## Reverse of a Regular Language [closed]

Hi all,

This is a homework. I want to know if I'm on the right way, The problem is: show that if L is a subset of sigma* is a regular language, then the following language is also a regular one:

$L^'$ ={w | there is x, y $\in \sigma*$ | w = xy $\wedge$ yx $\in$ to L}


To do that, I've constructed a NFA that accept L. Then I've inverted the transitions of the NFA so that it could accept the inverted language. I Made old initial state a final state, and then I added a new initial state.

Is that correct? Thanks.

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You should ask your instructor. Voted to close. – Mark Sapir Oct 13 2011 at 3:46
The title of your question and your proposed solution suggest that you misread the problem. Notice that, if $L$ contains, for example, abcde, then the definition says $L'$ will contain cdeab (by taking $x$ and $y$ to be cde and ab), but it does not say that $L'$ will contain $edcba$. – Andreas Blass Oct 13 2011 at 13:06