Define for a context free language
L ≤ {0 ; 1} init (L) = {u/uv ε L for some v in {0,1}}
(in other words, init (L) is the set of prefixes of L)
Let L {w/w is noempty and has an equal number of 0’s and 1’s)
Then init (L) is

A) set of all binary strings with unequal number of 0’s and 1’s

B) set of all binary strings including the null string

C) set of all binary strings with exactly one more 0’s than the number of 1’s or 1 more than the number of 0’s

D) set of all binary strings without null string

Option b is right answer.

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Define for a context free languageL ≤ {0 ; 1} init (L) = {u/uv ε L for some v in {0,1}}(in other words, init (L) is the set of prefixes of L)Let L {w/w is noempty and has an equal number of 0’s and 1’s)Then init (L) is