Build a Turing Machine for Language L = {a^nb^n:n≥m}

How does a Turing Machine work for the language L = {a^nb^n:n≥m}?

Would you like to build a Turing Machine for the language L = {a^nb^n:n≥m}?

Explanation:

In order to build a Turing Machine for the language L = {a^nb^n:n≥m}, we need to systematically replace 'b's with 'B' and 'a's with 'A' until they are all aligned properly. The Turing Machine works by reading the input tape from left to right and following a series of steps to achieve this alignment.

Building the Turing Machine:

A Turing Machine that accepts the language L = {a^nb^n:n≥m} can be constructed by following these steps:

1. Read the input tape from left to right.
2. Start in state q0.
3. Scan the input tape to find the first occurrence of the character 'b'.
4. Replace the first 'b' with a blank symbol (represented as 'B') and move to the right.
5. Scan the input tape to find the next occurrence of 'b' to the right of the previously replaced 'b'.
6. Replace this 'b' with 'B' and move to the right.
7. Repeat steps 5 and 6 until all 'b's to the right of the first replaced 'b' are replaced with 'B'.
8. Scan the input tape to find the first occurrence of the character 'a' to the right of the previously replaced 'b's.
9. Replace this 'a' with 'A' and move to the right.
10. Repeat steps 8 and 9 until all 'a's to the right of the previously replaced 'b's are replaced with 'A'.
11. Continue to repeat the process to align all 'a's and 'b's correctly.

This systematic approach ensures that the Turing Machine correctly processes the input tape and accepts it only if the number of 'a's and 'b's are equal and aligned as required by the language L = {a^nb^n:n≥m}.