**Turing Machine Design with Input Alphabet {a, b}***Objective*: Create a Turing machine with the input alphabet {a, b} that accepts a string if and only if the string has the specified property.*Property*: The input string contains more a's than b's. ### Detailed ExplanationIn order to design a Turing machine that accepts any string with more `a`s than `b`s, consider the following high-level steps:1. **Initialization**: - Start from the beginning of the tape and leave an indicator or marker (such as `*`) to know where you began.2. **Scan for Characters**: - Traverse the tape to find the first unmarked `a` and replace it with a special symbol (like `X` or `Y`) to indicate it has been processed. - Similarly, traverse the tape to find the first unmarked `b` and mark it similarly.3. **Balancing a's and b's**: - For each `a` marked, find a matching `b` and vice versa. If you manage to pair all `b`s but still have `a`s left, it means there are more `a`s than `b`s. - Conversely, if you pair all `a`s but have `b`s left, the string doesn't have more `a`s.4. **Final Check**: - If you reach the end of the tape with more `a`s marked than `b`s, stop and accept the string. - If `b`s exceed, the machine enters a reject state.### Example Algorithm:1. **Start State**: Traverse right looking for an `a` or `b`.2. **Marking an `a`**: - Upon finding an unmarked `a`, change it to `X` and move to a state to find a `b`.3. **Marking a `b`**: On finding an unmarked `b`, change it to `Y` and revert back to the state searching for an `a`. - Repeat the above two steps until all characters are marked.4. **Decision**: - Transition to the accept state if excess `a`s are found, else reject. ### Note:The machine relies on marking `a`s and `b`s to balance them. By the end of the traversal, the excess of

Start in the initial state.Read the input symbol.If the symbol is 'a', move to a state that counts…

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Design a Turing machine with input alphabet (a, b) that accepts a string if and only if the string has the property described. The input string has more a's than b's.

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Question

**Turing Machine Design with Input Alphabet {a, b}**

*Objective*:

Create a Turing machine with the input alphabet {a, b} that accepts a string if and only if the string has the specified property.

*Property*:

The input string contains more a's than b's.

### Detailed Explanation

In order to design a Turing machine that accepts any string with more `a`s than `b`s, consider the following high-level steps:

1. **Initialization**:
- Start from the beginning of the tape and leave an indicator or marker (such as `*`) to know where you began.

2. **Scan for Characters**:
- Traverse the tape to find the first unmarked `a` and replace it with a special symbol (like `X` or `Y`) to indicate it has been processed.
- Similarly, traverse the tape to find the first unmarked `b` and mark it similarly.

3. **Balancing a's and b's**:
- For each `a` marked, find a matching `b` and vice versa. If you manage to pair all `b`s but still have `a`s left, it means there are more `a`s than `b`s.
- Conversely, if you pair all `a`s but have `b`s left, the string doesn't have more `a`s.

4. **Final Check**:
- If you reach the end of the tape with more `a`s marked than `b`s, stop and accept the string.
- If `b`s exceed, the machine enters a reject state.

### Example Algorithm:
1. **Start State**: Traverse right looking for an `a` or `b`.
2. **Marking an `a`**:
- Upon finding an unmarked `a`, change it to `X` and move to a state to find a `b`.
3. **Marking a `b`**: On finding an unmarked `b`, change it to `Y` and revert back to the state searching for an `a`.
- Repeat the above two steps until all characters are marked.
4. **Decision**:
- Transition to the accept state if excess `a`s are found, else reject.

### Note:
The machine relies on marking `a`s and `b`s to balance them. By the end of the traversal, the excess of

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