Let L be an arbitrary regular language over the alphabet $\backslash$Sigma $=\{0,1\}.$ Prove that the following

languages are also regular. $($You probably won$$t get to all of these.$)$ cycle$($L$)$ :$=\{$x y$|$x$,$ y in $\backslash$Sigma $,$ y x in L$\},$ The language that accepts the rotations of string from

a regular language