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Design a Turing machine M that decides the language L = {0"1" |n>0}.

Design a Turing machine M that decides the language L = {0"1" |n>0}.

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:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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**Designing a Turing Machine to Decide a Language** **Problem Statement:** Design a Turing machine \( M \) that decides the language \( L = \{ 0^n 1^n \mid n \geq 0 \} \). **Explanation:** The task is to create a Turing machine that accepts strings consisting of \( n \) zeros followed by \( n \) ones, where \( n \) is a non-negative integer. For example, the strings "", "01", "0011", and "000111" are in the language, while "10", "001", and "010" are not. **Approach:** 1. **Input and Validation:** - The input tape contains a string of the format \( 0^n 1^n \). - The Turing machine will check if the number of 0s is equal to the number of 1s. 2. **Basic Steps:** - Start by reading the first 0, then change it to a special symbol (e.g., X) to mark it as processed. - Move right to find the first unmarked 1 and change it to a special symbol (e.g., Y). - Return to the left-most unprocessed 0 and repeat the process. - Continue marking until there are no unprocessed 0s or 1s left. - If the above process uniquely matches every 0 with a 1, the string is in the language. - If there is a mismatch (an unprocessed 0 or 1 remains), the string is not in the language. 3. **Acceptance Criteria:** - The machine halts and accepts if every 0 has a corresponding 1. - The machine halts and rejects if any unprocessed 0 or 1 is left. This design ensures the correct operation of the Turing machine \( M \) for the language \( L = \{ 0^n 1^n \mid n \geq 0 \} \).
Transcribed Image Text:**Designing a Turing Machine to Decide a Language** **Problem Statement:** Design a Turing machine \( M \) that decides the language \( L = \{ 0^n 1^n \mid n \geq 0 \} \). **Explanation:** The task is to create a Turing machine that accepts strings consisting of \( n \) zeros followed by \( n \) ones, where \( n \) is a non-negative integer. For example, the strings "", "01", "0011", and "000111" are in the language, while "10", "001", and "010" are not. **Approach:** 1. **Input and Validation:** - The input tape contains a string of the format \( 0^n 1^n \). - The Turing machine will check if the number of 0s is equal to the number of 1s. 2. **Basic Steps:** - Start by reading the first 0, then change it to a special symbol (e.g., X) to mark it as processed. - Move right to find the first unmarked 1 and change it to a special symbol (e.g., Y). - Return to the left-most unprocessed 0 and repeat the process. - Continue marking until there are no unprocessed 0s or 1s left. - If the above process uniquely matches every 0 with a 1, the string is in the language. - If there is a mismatch (an unprocessed 0 or 1 remains), the string is not in the language. 3. **Acceptance Criteria:** - The machine halts and accepts if every 0 has a corresponding 1. - The machine halts and rejects if any unprocessed 0 or 1 is left. This design ensures the correct operation of the Turing machine \( M \) for the language \( L = \{ 0^n 1^n \mid n \geq 0 \} \).
**Educational Content with Transition Diagram** --- ### Problem Statement: (2) Define M with a transition diagram. You may use JFLAP to create this diagram. Compare your diagram with the following and verify its correctness. Note that there can be multiple correct answers. ### Machine Specification: \[ M = (\{q_0, q_1, q_2, q_3, y\}, \{0, 1\}, \{0, 1, \$, \#, \square\}, \delta, q_0, \{y\}) \] Where the transition function \( \delta \) is defined in the diagram below. ### Transition Diagram Description: - **States**: \( q_0, q_1, q_2, q_3, \text{yes} \) - **Alphabet**: \( \{0, 1\} \) - **Tape Symbols**: \( \{0, 1, \$, \#, \square\} \) #### Transition Details: - **State \( q_0 \)** (Start State): - \( 0 \) transitions to \( q_0 \) with write symbol \$ and move right. - \$ transitions to \( q_1 \) with write symbol \$ and move right. - \# transitions to \( q_3 \) with write symbol \# and move right. - **State \( q_1 \)**: - \( 0 \) transitions to \( q_1 \) with write symbol 0 and move right. - \# transitions to \( q_2 \) with write symbol \# and move left. - **State \( q_2 \)**: - 1 transitions to \( q_1 \) with write symbol \# and move left. - 0 transitions to \( q_2 \) with write symbol 0 and move left. - **State \( q_3 \)**: - \# transitions to \( q_3 \) with write symbol \# and move right. - \( \square \) transitions to \text{yes} with write symbol \( \square \) and move right. - **State \text{yes}** (Accept State): - Accepts the input. ### Conclusion: Verify the correctness of your transition diagram against the described transitions. Adjust your diagram as needed to ensure all transitions align with the specified
Transcribed Image Text:**Educational Content with Transition Diagram** --- ### Problem Statement: (2) Define M with a transition diagram. You may use JFLAP to create this diagram. Compare your diagram with the following and verify its correctness. Note that there can be multiple correct answers. ### Machine Specification: \[ M = (\{q_0, q_1, q_2, q_3, y\}, \{0, 1\}, \{0, 1, \$, \#, \square\}, \delta, q_0, \{y\}) \] Where the transition function \( \delta \) is defined in the diagram below. ### Transition Diagram Description: - **States**: \( q_0, q_1, q_2, q_3, \text{yes} \) - **Alphabet**: \( \{0, 1\} \) - **Tape Symbols**: \( \{0, 1, \$, \#, \square\} \) #### Transition Details: - **State \( q_0 \)** (Start State): - \( 0 \) transitions to \( q_0 \) with write symbol \$ and move right. - \$ transitions to \( q_1 \) with write symbol \$ and move right. - \# transitions to \( q_3 \) with write symbol \# and move right. - **State \( q_1 \)**: - \( 0 \) transitions to \( q_1 \) with write symbol 0 and move right. - \# transitions to \( q_2 \) with write symbol \# and move left. - **State \( q_2 \)**: - 1 transitions to \( q_1 \) with write symbol \# and move left. - 0 transitions to \( q_2 \) with write symbol 0 and move left. - **State \( q_3 \)**: - \# transitions to \( q_3 \) with write symbol \# and move right. - \( \square \) transitions to \text{yes} with write symbol \( \square \) and move right. - **State \text{yes}** (Accept State): - Accepts the input. ### Conclusion: Verify the correctness of your transition diagram against the described transitions. Adjust your diagram as needed to ensure all transitions align with the specified
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