Palindrome mean that can be even palindrome or that can be odd palindrome
In even palindrome say L = w wr where we need to give a transition (in between with the help of ∊) after which we know reverse get started.
L= w ∊ wr [eq: ababbaba as abab∊baba ]
before ∊ we need to push symbols in stack , after∊we need to pop symbol from stack
PUSH operation
$\delta$(q,a,Z) =$\delta$(q, aZ)
$\delta$(q,b,Z) =$\delta$(q, bZ)
$\delta$(q,a,a) =$\delta$(q, aa)
$\delta$(q,b,b) =$\delta$(q, bb)
$\delta$(q,a,b) =$\delta$(q, ab)
$\delta$(q,b,a) =$\delta$(q, ba)
then DONOTHING
$\delta$(q,∊,a )= (q1,a)
$\delta$(q,∊,b )= (q1,b) [State change with ∊ , a Mark now we will get wr, so we need to do POP]
then POP operations
$\delta$(q1,a,a) = (q1, ∊)
$\delta$(q1,b,b)= (q1,∊)
Then acceptance
$\delta$(q1,∊,Z) = (qf ,∊)
So Palindrome is NCFL
Note: we talk about L= { wcwr | w∊ (a,b)* } that is DCFL ,