Building a Turing Machine to Accept the Language L = {a^nb^m : n, m ≥ 0}

How can a Turing Machine be constructed to accept the language L = {a^nb^m : n, m ≥ 0}?

By following the steps outlined above, a Turing Machine can be built to accept the language L = {a^nb^m : n, m ≥ 0}. It counts the number of 'a's and 'b's in the input string and compares them to determine if the string belongs to the language.

Answer:

A Turing Machine can be built to accept the language L = {a^nb^m : n, m ≥ 0} by following these steps:

1. Start at the beginning of the input string.
2. Scan the input tape to count the number of 'a's in the string.
3. If an 'a' is found, replace it with a special symbol (let's say 'X') and move to the right.
4. Repeat steps 2 and 3 until all 'a's have been replaced.
5. Move to the right until the end of the input tape is reached.
6. Scan the remaining symbols on the input tape to count the number of 'b's.
7. If a 'b' is found, move to the right without making any changes.
8. Repeat step 7 until the end of the input tape is reached.
9. If the end of the input tape is reached, and the number of 'b's is greater than or equal to the number of 'X's, the Turing Machine accepts the input string. Otherwise, it rejects the input string.

The Turing Machine starts by counting the number of 'a's in the input string. It replaces each 'a' with a special symbol 'X' to keep track of the count. Then it moves to the right until the end of the input tape. Next, the Turing Machine counts the number of 'b's on the remaining symbols of the input tape. It does not modify the 'b's, but only moves to the right until the end of the input tape. After reaching the end of the input tape, the Turing Machine checks if the number of 'b's is greater than or equal to the number of 'X's. If it is, then the input string belongs to the language L and the Turing Machine accepts it. Otherwise, the input string does not belong to the language L and the Turing Machine rejects it.

This process ensures that the input string contains any number of 'a's followed by any number of 'b's, satisfying the condition n, m ≥ 0.