Question: Let Lk { 0 , 1 } be the language defined as Lk = { xy | x , y in { 0 , 1

Let Lk {0,1}
be the language defined as
Lk ={xy | x, y in {0,1}
k
, and the bitwise-AND of x and y is 0
k
}.
Observe that Lk is finite, and hence, regular. Prove that for all k, any NFA that recognizes Lk has at least
2
k
states.

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