00:01
So, let's look at the question.
00:01
We have to prove that the language l for a n b n c i 0 where i is greater than or equal to n which is less than 0 and i is less than or equal to n plus 1 is not context free using the pumping lemma.
00:23
We assume that l is context free and reach a contradiction.
00:27
According to the pumping lemma for context free languages, there exists a constant p the pumping length such that the string s in l with the length at least p can be divided into 5 parts that is s is equal to u v x y z satisfying the following condition for one for each i is greater than or equal to 0 or u v to the power i x y to the power i z is belonging to l.
01:10
Second, r mod v x y is less than or equal to p.
01:15
Third, r mod v and y is greater than 0.
01:19
Now, let's choose the string s which is equals to a to the power p b to the power p and c to the power p plus 1.
01:31
The string s in l and has a length of at least p.
01:35
According to the pumping lemma s can be divided into u v x y z such that it satisfies three conditions mentioned above...