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CMI2021-B: 4

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For a language $\text{L}$ over an alphabet $\Sigma$, define

$$\text{SW(L)}:= \left \{ y \in \Sigma^{\ast} \mid \exists x \in \Sigma^{\ast}\; \text{s.t.}\; xyx \in \text{L} \right \}$$

Prove that if  $\text{L}$ is regular, $\text{SW(L)}$ is also regular.
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