00:01
So, in this question, let's design context -free grammars for the given language.
00:04
So, in the a part, 0 to the power n, 1 to the power n, where n greater than equal to 1.
00:13
So, context -free grammar is s, 0, s1, 0, 1.
00:20
This grammar generates a string of the form 0 to the power n, 1 to the power n, where there is at least one 0 followed by the same number of 1s.
00:30
And s is the start symbol.
00:32
The production s, 0, s1 represent the recursive part of the grammar, ensuring that there is at least one 0 followed by the same number of 1s.
00:42
And the production s, 0, 1 is the base case, which ensures that there is at least one 0 followed by 1.
00:52
Now, coming to the b part of this question, that is, a to the power i, b to the power j, c to the power k, where i, j, k are not equal.
01:01
So, context -free grammar is s, x, y, y, x, x, a, x, b, epsilon, y, b, y, c, epsilon.
01:13
Here s is the start symbol...