Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN: 9780133594140
Author: James Kurose, Keith Ross
Publisher: PEARSON
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**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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Transcribed Image Text:**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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