For languages A and B, let the 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 shuffle.
Can you please help me with this problem because I am struggling on how to do this problem, which I don't understand what to do. Can you show something visual to represent the question and can you please explain the question leading up to the answer.
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What is needed here is to start with two DFAs M_A and M_B accepting regular languages A and B. Then you need to construct a new machine M from M_A and M_B possibly adding some states and arrows to make sure that this new machine accepts the shuffle of A and B.
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1.42 For languages A and B, let the shuffle of A and B be the language {w| w = a1b1 · · · akbk, where a1 · · · ak ∈ A and b1 · · · bk ∈ B, each
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