For languages A and B, let the perfect shuffle of A and B be the language {w|

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For languages A and B, let the perfect shuffle of A and B be the language

{w| w = a1b1 · · · akbk, where a1 · · · ak ∈ A and b1 · · · bk ∈ B, each ai, bi ∈ Σ}.

Show that the class of regular languages is closed under perfect shuffle.

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