Answer
See the explanation
Work Step by Step
Here's a high-level description of a Turing machine that detects palindromes:
1. **Initialization**: The Turing machine starts at the leftmost symbol of the input string.
2. **Read and Move to the End**: It reads the symbol and moves to the right end of the input string.
3. **Comparison**: While moving to the right end, it simultaneously compares the symbol it reads with the symbol at the corresponding position from the left end.
4. **Check for Equality**: If the symbols match, the Turing machine continues moving towards the middle of the input string. If the symbols don't match at any point, it halts and returns false (0).
5. **Palindrome Check**: Once it reaches the middle of the string (or approximately halfway, depending on the length of the string), it halts and returns true (1) if all symbols matched, indicating that the input string is a palindrome. Otherwise, it returns false (0).
6. **Halt**: After reaching the middle of the string and completing the comparison, the Turing machine halts.
This Turing machine design ensures that every symbol from the left end is compared with the corresponding symbol from the right end, effectively determining whether the input string is a palindrome or not.
