Let A, be the language defined as follows: A1 ={ xe{0,1}" | the number of Os in x is 4k+1 for some integer k} Which of the following regular expressions represents A,? O (1'01'01'01'01)y01 O 1'0(1'01'01'01'01) O 1'0(1'00001")" O (1'01'01'01'01")o

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
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**Problem Statement**

Let \( A_1 \) be the language defined as follows:

\[ A_1 = \{ x \in \{0,1\}^* \mid \text{the number of 0s in } x \text{ is } 4k+1 \text{ for some integer } k \} \]

Which of the following regular expressions represents \( A_1 \)?

**Options:**

1. \((1^*01^*01^*01^*01^*)^*\)

2. \(1^*0(1^*01^*01^*01^*)^*\)

3. \(1^*0(1^*0000)^*\)

4. \((1^*01^*01^*01^*01^*)^*0\)
Transcribed Image Text:**Problem Statement** Let \( A_1 \) be the language defined as follows: \[ A_1 = \{ x \in \{0,1\}^* \mid \text{the number of 0s in } x \text{ is } 4k+1 \text{ for some integer } k \} \] Which of the following regular expressions represents \( A_1 \)? **Options:** 1. \((1^*01^*01^*01^*01^*)^*\) 2. \(1^*0(1^*01^*01^*01^*)^*\) 3. \(1^*0(1^*0000)^*\) 4. \((1^*01^*01^*01^*01^*)^*0\)
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