GATE | GATE CS 1996 | Question 34

Define for a context free language L ⊆ {0, 1}* ,  init(L)={uuv ∈ L for some v in {0,1}∗} ( in other words, init(L) is the set of prefixes of L)

Let L = {w ∣ w is nonempty and has an equal number of 0’s and 1’s}
Then init(L) is
(A) the set of all binary strings with unequal number of 0’s and 1’s
(B) the set of all binary strings including null string
(C) the set of all binary strings with exactly one more 0 than the number of 1’s or one more 1 than the number of 0’s
(D) None of the above


Answer: (C)

Explanation:

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