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The regular expression r = (0+1)" O (0+1)* 0 (0-1)* denotes the language of the set of all strings containing at most two zeros. Select one: O True O False

The regular expression r = (0+1)" O (0+1)* 0 (0-1)* denotes the language of the set of all strings containing at most two zeros. Select one: O True O False

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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### Regular Expressions and Language Sets **Question:** The regular expression \( r = (0 + 1)^* \, 0 \, (0 + 1)^* \, 0 \, (0 + 1)^* \) denotes the language of the set of all strings containing at most two zeros. Select one: - ○ True - ○ False **Explanation:** The regular expression \( r \) is composed of the following components: - \( (0 + 1)^* \): This part denotes that any combination of the characters '0' and '1' can occur zero or more times. - \( 0 \): This part ensures that there is a '0' in the string. - \( (0 + 1)^* \) (repeated twice): These parts again denote any combination of the characters '0' and '1' occurring zero or more times. In total, the regular expression \( (0 + 1)^* \, 0 \, (0 + 1)^* \, 0 \, (0 + 1)^* \) denotes the set of all strings where there are two '0's, with any combination of '1's and other '0's allowed in between or around them. The question asks whether the regular expression denotes the language of the set of all strings containing **at most** two zeros. Given that the regular expression specifically specifies exactly two zeros, the correct answer would be **False**, because it does not cater to strings with fewer than two zeros. --- This explanation provides the necessary context for understanding how the regular expression operates and what it denotes in terms of string patterns within a language set.
Transcribed Image Text:### Regular Expressions and Language Sets **Question:** The regular expression \( r = (0 + 1)^* \, 0 \, (0 + 1)^* \, 0 \, (0 + 1)^* \) denotes the language of the set of all strings containing at most two zeros. Select one: - ○ True - ○ False **Explanation:** The regular expression \( r \) is composed of the following components: - \( (0 + 1)^* \): This part denotes that any combination of the characters '0' and '1' can occur zero or more times. - \( 0 \): This part ensures that there is a '0' in the string. - \( (0 + 1)^* \) (repeated twice): These parts again denote any combination of the characters '0' and '1' occurring zero or more times. In total, the regular expression \( (0 + 1)^* \, 0 \, (0 + 1)^* \, 0 \, (0 + 1)^* \) denotes the set of all strings where there are two '0's, with any combination of '1's and other '0's allowed in between or around them. The question asks whether the regular expression denotes the language of the set of all strings containing **at most** two zeros. Given that the regular expression specifically specifies exactly two zeros, the correct answer would be **False**, because it does not cater to strings with fewer than two zeros. --- This explanation provides the necessary context for understanding how the regular expression operates and what it denotes in terms of string patterns within a language set.
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