We have automat $A$ for language $L$. Construct automat for $Cycle(L)$ where $Cycle(L)=\{uv:vu\in L\}$.
I have a problem with this exercise. Help me, please.
Edit
$A = (Q_A, \Sigma, \delta, q_0, F_A)$- automat for language $L$
$A'$ - copy of automat $A$ such that there is no accept state and every state is beginning state. For each state $ (q,q')\in Q_{A'} $ we create copy of $A$ $(A_{q})$ such that only accepting state is $q$.
$A'=(Q_{A'},\Sigma, \delta', Q_{A'}, \emptyset)$
$Q_{A'}=Q\times Q $
$\delta'((q_1, q_2), a\in \Sigma)=(\delta(q_1, a), q_1) $
$\delta'((q_1, q_2), \epsilon)= q_0 \in A_{q_2} \text{ where $q_1$$\in$ $F_A$ }$