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

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

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Design a Turing Machine** Design a Turing machine \( M \) that decides the language \( L = \{ 0^n 1^n \mid n \geq 1 \} \). This design requires a Turing machine \( M \) to accept strings composed of consecutive zeros followed by an equal number of ones, ensuring that the number of zeros is the same as the number of ones. For example, strings like "01", "0011", and "000111" should be accepted, while strings like "10", "011", or "00011" should not. The Turing machine will have to process the input and keep track of corresponding 0s and 1s to either accept or reject the input string based on the criteria above.
Transcribed Image Text:**Design a Turing Machine** Design a Turing machine \( M \) that decides the language \( L = \{ 0^n 1^n \mid n \geq 1 \} \). This design requires a Turing machine \( M \) to accept strings composed of consecutive zeros followed by an equal number of ones, ensuring that the number of zeros is the same as the number of ones. For example, strings like "01", "0011", and "000111" should be accepted, while strings like "10", "011", or "00011" should not. The Turing machine will have to process the input and keep track of corresponding 0s and 1s to either accept or reject the input string based on the criteria above.
**High-Level Description of M** **Task:** Verify the correctness of the answer to the given question. **Algorithm Steps:** 1. **Move right.** 2. **Loop:** 2.1. If the current symbol is 0, change it to $ and move right. If not, exit the loop. 2.2. Scan rightwards, passing 0's and #'s, to find a 1. 2.3. If a 1 is found, change it to # and move left. Otherwise, reject. 2.4. Scan leftwards, passing 0's and #'s, to find a $. 2.5. Upon finding the first $, move right and return to step 2.1. 3. If the current symbol is #, move right. If not, reject. 4. Scan rightwards, passing #'s, to find the blank symbol. 5. Upon finding the first blank symbol, move right and accept. **Verification:** - [ ] The provided answer is correct. - [ ] The provided answer is incorrect.
Transcribed Image Text:**High-Level Description of M** **Task:** Verify the correctness of the answer to the given question. **Algorithm Steps:** 1. **Move right.** 2. **Loop:** 2.1. If the current symbol is 0, change it to $ and move right. If not, exit the loop. 2.2. Scan rightwards, passing 0's and #'s, to find a 1. 2.3. If a 1 is found, change it to # and move left. Otherwise, reject. 2.4. Scan leftwards, passing 0's and #'s, to find a $. 2.5. Upon finding the first $, move right and return to step 2.1. 3. If the current symbol is #, move right. If not, reject. 4. Scan rightwards, passing #'s, to find the blank symbol. 5. Upon finding the first blank symbol, move right and accept. **Verification:** - [ ] The provided answer is correct. - [ ] The provided answer is incorrect.
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