Important Exercise and Solutions


Identify the language:




This same problem already discussed in Example 2 please see for details.


And because there is no special character so, it needs multiple copies of the stack. 

For details see Example 2.




The type of language is similar to the above language. 

Example: abbabba

But in the previous example, it was even palindrome.

But here same like the previous example, we need multiple copies of the machine because middle (a + b) is not working as a special character, it also part of the string where ∑ = {a, b}.


In that case, is the same previous example we can’t recognize – 

We should create various copies of machines


This language also a set of palindrome but in that case all palindrome string (even and odd) i.e. set of all even and odd palindrome string.

Previously we have already seen a set of even palindrome and set odd palindrome distinctly.

Now it is a set of all palindrome string (even and odd), Example: abba, aba


Set of all even palindrome – one machine work for it

Set of all odd palindrome – one machine work for this


In this case, also we need multiple copies of the machine.



We already solve the same problem in Example 1 please see the details

Because of the special symbol # which is not a direct part of the language (not belongs to ), we can identify which one is an original string and which is a reverse string.


So, by a single stack, we can solve the problem i.e. push and pop are cleared.

Because of one comparison and push, pop is cleared.