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Show that the regular languages are closed under the following operation$:$ $\text{cycle(L)={we can write w as w = xy,such that yx is in L}}.$ For example if $L=\{01,011\},$then $cycle(L)=\{01,10,011,110,101\}.$  Hint$:$ Start with a DFA for $L$ and construct an $\in-NFA$ for $cycle(L).$
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