Sipser 2.45 Let A = {wtwR | w,t ∈ {0,1}* and |w| = |t|}. Prove that A is not context free language.

2.45 Let A = {wtw^R | w,t ∈ {0,1}* and |w| = |t|}. Prove that A is not context free language.

Solution:
Consider a string 1^2p(01)^p1^2p, where p is the pumping length. If you pump up only in leftmost 1^2p then number of 1's will be not equal to rightmost 1^2p. Similarly if pumped from leftmost 1^2p.
If we pump up somewhere in (01)^p, then we must have to consider (2p+1)st element from left and right in w and w^R but (2p+1)st from left will be a 0 and and (2p+1)st from right it will be a 1.
If I pump across boundary 1^2p(01)^p such that v is in 1^2p and y is in (01)^p. In this case pump up twice, we will see that (2p+2)nd symbol from left is 1 and from right is 0.