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Consider the following regular expressions over the alphabet {0, 1}.
I. 1* 0(0 + 1)*
II. (0 + 1)* 01*
III. 1* 0(1 + 0)* + (0 + 1)* 01*
Which of the above regular expressions are equivalent?
- a)I and III only
- b)I and II only
- c)II and III only
- d)I, II and III
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following regular expressions over the alphabet {0, 1}.I...
I and II are quite easy to understand - both denote strings containing at least one 0. III is actually the union of I and II, but III is again denoting strings containing at least one 0, as both regular expressions (i.e. I and II) are equivalent, so union won't make any difference.
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Hence all 3 regular expressions are equivalent.
Most Upvoted Answer
Consider the following regular expressions over the alphabet {0, 1}.I...
To determine which of the given regular expressions are equivalent, we need to analyze each expression and compare their language descriptions.
I. 1* 0(0 1)*
This regular expression describes the language that starts with zero or more ones (1*), followed by a single zero (0), and ends with zero or more occurrences of either zero or one ((0 1)*). This expression represents strings that start with any number of ones and end with any combination of zeros and ones. For example, it matches strings like "100", "1111001", "1110", etc.
II. (0 1)* 01*
This regular expression describes the language that starts with zero or more occurrences of either zero or one ((0 1)*), followed by a single zero (0), and ends with zero or more ones (1*). This expression represents strings that start with any combination of zeros and ones and end with any number of ones. For example, it matches strings like "10", "001", "11110", etc.
III. 1* 0(1 0)* (0 1)* 01*
This regular expression describes the language that starts with zero or more ones (1*), followed by a single zero (0), followed by zero or more occurrences of either one or zero ((1 0)*), followed by zero or more occurrences of either zero or one ((0 1)*), and ends with a single zero (0) and zero or more ones (1*). This expression represents strings that start with any number of ones, followed by a zero, followed by any combination of ones and zeros, followed by any combination of zeros and ones, and ends with a zero and any number of ones. For example, it matches strings like "100", "11100101", "11100001", etc.
To determine which regular expressions are equivalent, we can compare the languages described by each expression. By analyzing the language descriptions, we can see that:
- Expression I describes strings that start with any number of ones and end with any combination of zeros and ones.
- Expression II describes strings that start with any combination of zeros and ones and end with any number of ones.
- Expression III describes strings that start with any number of ones, followed by a zero, followed by any combination of ones and zeros, followed by any combination of zeros and ones, and ends with a zero and any number of ones.
Comparing the language descriptions, we can see that expressions I and II are not equivalent because they describe different patterns of zeros and ones at the start and end of the strings. However, expression III includes both patterns described by expressions I and II, making it equivalent to both of them.
Therefore, the correct answer is option D: I, II, and III are all equivalent.
I. 1* 0(0 1)*
This regular expression describes the language that starts with zero or more ones (1*), followed by a single zero (0), and ends with zero or more occurrences of either zero or one ((0 1)*). This expression represents strings that start with any number of ones and end with any combination of zeros and ones. For example, it matches strings like "100", "1111001", "1110", etc.
II. (0 1)* 01*
This regular expression describes the language that starts with zero or more occurrences of either zero or one ((0 1)*), followed by a single zero (0), and ends with zero or more ones (1*). This expression represents strings that start with any combination of zeros and ones and end with any number of ones. For example, it matches strings like "10", "001", "11110", etc.
III. 1* 0(1 0)* (0 1)* 01*
This regular expression describes the language that starts with zero or more ones (1*), followed by a single zero (0), followed by zero or more occurrences of either one or zero ((1 0)*), followed by zero or more occurrences of either zero or one ((0 1)*), and ends with a single zero (0) and zero or more ones (1*). This expression represents strings that start with any number of ones, followed by a zero, followed by any combination of ones and zeros, followed by any combination of zeros and ones, and ends with a zero and any number of ones. For example, it matches strings like "100", "11100101", "11100001", etc.
To determine which regular expressions are equivalent, we can compare the languages described by each expression. By analyzing the language descriptions, we can see that:
- Expression I describes strings that start with any number of ones and end with any combination of zeros and ones.
- Expression II describes strings that start with any combination of zeros and ones and end with any number of ones.
- Expression III describes strings that start with any number of ones, followed by a zero, followed by any combination of ones and zeros, followed by any combination of zeros and ones, and ends with a zero and any number of ones.
Comparing the language descriptions, we can see that expressions I and II are not equivalent because they describe different patterns of zeros and ones at the start and end of the strings. However, expression III includes both patterns described by expressions I and II, making it equivalent to both of them.
Therefore, the correct answer is option D: I, II, and III are all equivalent.
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Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer?
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Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the following regular expressions over the alphabet {0, 1}.I. 1* 0(0 + 1)*II. (0 + 1)* 01*III. 1* 0(1 + 0)* + (0 + 1)* 01*Which of the above regular expressions are equivalent?a)I and III onlyb)I and II onlyc)II and III onlyd)I, II and IIICorrect answer is option 'D'. Can you explain this answer?.
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