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Let A be the language defined as follows: A ={ xe{0,1}* | the number of Os in x is 4k+1 or 4k+2 for some integer k Which of the following regular expressions represents A? O (1°01'01°01 01")r01) U ((1*01 01 01*01*)*01*01*) O (10) U (1'01 0)(1*00001")* (1"01"01'01"01") (01")U (01°01") o (1*0(1*01 01"01"01)") U (1*0(1*01*01*01*01*)*01*) O 0(1*01*01'01"01")0

Let A be the language defined as follows: A ={ xe{0,1}* | the number of Os in x is 4k+1 or 4k+2 for some integer k Which of the following regular expressions represents A? O (1°01'01°01 01")r01) U ((1*01 01 01*01*)*01*01*) O (10) U (1'01 0)(1*00001")* (1"01"01'01"01") (01")U (01°01") o (1*0(1*01 01"01"01)") U (1*0(1*01*01*01*01*)*01*) O 0(1*01*01'01"01")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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**Language Definition and Regular Expression Problem** **Problem Definition:** Let \( A \) be the language defined as follows: \[ A = \{ x \in \{0,1\}^* \mid \text{the number of 0s in } x \text{ is } 4k+1 \text{ or } 4k+2 \text{ for some integer } k \} \] **Question:** Which of the following regular expressions represents the language \( A \)? **Options:** 1. \((1^*01^*01^*01^*01^*) \cup (1^*01^*01^*01^*01^*01^*)\) 2. \((1^*0) \cup (1^*01^*0)(1^*00001^*)^*\) 3. \(1^*01^*01^*01^*((01^*) \cup (01^*01))\) 4. \((1^*01^*01^*01^*01^*) \cup (1^*01^*01^*01^*01^*01^*01^*)\) 5. \(0^*1^*01^*01^*01^*01^*0\) **Explanation of the Problem:** The question asks us to identify which regular expression matches the language \( A \), where the sequence consists of binary strings with the number of 0s being either \( 4k+1 \) or \( 4k+2 \) for some integer \( k \). **Explanation of Choices:** 1. **Option 1:** Repeated sequence of blocks with four and five "01" patterns, corresponding to possible counts of '0' being \( 4k+1 \) or \( 4k+2 \). 2. **Option 2:** Initial option combined with an additional zero, suggesting a form of counting of zeros. 3. **Option 3:** Variably builds the expression with sequences that logically group patterns of one or two repetitions of certain sequences. 4. **Option 4:** Larger repetition and combination of sequences indicating separate instances that might fit the criteria. 5. **Option 5:** Suggests a possible singular sequence but likely does not cover the full breadth of possibilities. Understanding these options requires familiarity with the rules of
Transcribed Image Text:**Language Definition and Regular Expression Problem** **Problem Definition:** Let \( A \) be the language defined as follows: \[ A = \{ x \in \{0,1\}^* \mid \text{the number of 0s in } x \text{ is } 4k+1 \text{ or } 4k+2 \text{ for some integer } k \} \] **Question:** Which of the following regular expressions represents the language \( A \)? **Options:** 1. \((1^*01^*01^*01^*01^*) \cup (1^*01^*01^*01^*01^*01^*)\) 2. \((1^*0) \cup (1^*01^*0)(1^*00001^*)^*\) 3. \(1^*01^*01^*01^*((01^*) \cup (01^*01))\) 4. \((1^*01^*01^*01^*01^*) \cup (1^*01^*01^*01^*01^*01^*01^*)\) 5. \(0^*1^*01^*01^*01^*01^*0\) **Explanation of the Problem:** The question asks us to identify which regular expression matches the language \( A \), where the sequence consists of binary strings with the number of 0s being either \( 4k+1 \) or \( 4k+2 \) for some integer \( k \). **Explanation of Choices:** 1. **Option 1:** Repeated sequence of blocks with four and five "01" patterns, corresponding to possible counts of '0' being \( 4k+1 \) or \( 4k+2 \). 2. **Option 2:** Initial option combined with an additional zero, suggesting a form of counting of zeros. 3. **Option 3:** Variably builds the expression with sequences that logically group patterns of one or two repetitions of certain sequences. 4. **Option 4:** Larger repetition and combination of sequences indicating separate instances that might fit the criteria. 5. **Option 5:** Suggests a possible singular sequence but likely does not cover the full breadth of possibilities. Understanding these options requires familiarity with the rules of
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