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(Solved): Problem 4 (Sipser Problem 1.42). 1.42 For languages A and B, let the shuffle of A and B be the langu ...



Problem 4 (Sipser Problem 1.42). 1.42 For languages

A

and

B

, let the shuffle of

A

and

B

be the language

{(w|w

|

=a_(1)b_(1)cdotsa_(k)b_(k)):}

, where

a_(1)cdotsa_(k)inA

and

b_(1)cdotsb_(k)inB

, each

{:a_(i),b_(i)in\Sigma ^(**)}

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



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