Question

Design Turing Machine for the following

L = {ww^R | w E {0, 1}* and |v| = 2 x |u|}

based on palindromes

Answer 1

Answer 2

Answer:

A Turing Machine (TM) for $L=\{{\text{ww}}^R\mid w\in \{0,1{\}}^{\ast }\}$ (even-length palindromes) works as follows:

Steps:

1. Check Even Length:

• Traverse the tape to ensure input length is even (reject if odd).

• 
  

2. Match & Flip:

• Cross off the first symbol (0 or 1) and remember it.

• Move right to the last uncrossed symbol, verify it matches, and cross it off.

• Repeat until the entire string is processed.

3. Accept: If all pairs match symmetrically.

4. 
   

Example (Input: 0110)

• Step 1: Cross off first 0, last 0 → X11X.

• Step 2: Cross off first 1, last 1 → XXXX → Accept.

• 
  

Final State: Accept if the entire string is crossed off symmetrically.