Question: For a string a 1 a 2 . . . an define the operation shift as shift ( a 1 a 2 . . .

For a string a1a2...an define the operation shift as shift(a1a2...an)=a2...ana1.
From this, we can define the operation on a language as shift(L)={v:v=shift(w) for some w in L}.
Show that regularity is preserved under the shift operation.

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