Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > For S->0S1|e for ∑={0,1}*, which of th...
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For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?
- a)Non regular language
- b)0n1n | n > = 0
- c)0n1n | n > = 1
- d)None of the mentioned
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
For S->0S1|e for ∑={0,1}*, which of the following is wrong for ...
L = {e, 01, 0011, 000111, ……0n1n}. As epsilon is a part of the set, thus all the options are correct implying none of them to be wrong.
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For S->0S1|e for ∑={0,1}*, which of the following is wrong for ...
Understanding the Language Generated by the Grammar
The given grammar S -> 0S1 | e generates a specific type of language over the alphabet Σ = {0, 1}. Let's analyze the structure and implications of this grammar.
Language Structure
- The grammar produces strings that consist of an equal number of 0s followed by an equal number of 1s.
- The empty string (e) is also a valid string in this language, which indicates that n can be zero.
Language Characteristics
- The language can be represented as L = { 0^n 1^n | n >= 0 }. This means:
- For n = 0, the string is e (the empty string).
- For n = 1, the string is "01".
- For n = 2, the string is "0011", and so on.
- Thus, option b (0^n 1^n | n >= 0) correctly describes the language.
Analyzing the Options
- Option a: Non-regular language
- This is correct; the language is non-regular because it cannot be represented by a regular expression or finite automaton.
- Option b: 0^n 1^n | n >= 0
- This is correct. As explained above, the grammar generates this language.
- Option c: 0^n 1^n | n >= 1
- This is incorrect because it excludes the empty string. The grammar allows n to be 0, making this option false.
- Option d: None of the mentioned
- This is correct because the only incorrect statement is option c.
Conclusion
Thus, option d is indeed the correct answer, as it acknowledges that the statements regarding the language produced by the grammar are valid, except for option c. The language is non-regular and includes the empty string.
The given grammar S -> 0S1 | e generates a specific type of language over the alphabet Σ = {0, 1}. Let's analyze the structure and implications of this grammar.
Language Structure
- The grammar produces strings that consist of an equal number of 0s followed by an equal number of 1s.
- The empty string (e) is also a valid string in this language, which indicates that n can be zero.
Language Characteristics
- The language can be represented as L = { 0^n 1^n | n >= 0 }. This means:
- For n = 0, the string is e (the empty string).
- For n = 1, the string is "01".
- For n = 2, the string is "0011", and so on.
- Thus, option b (0^n 1^n | n >= 0) correctly describes the language.
Analyzing the Options
- Option a: Non-regular language
- This is correct; the language is non-regular because it cannot be represented by a regular expression or finite automaton.
- Option b: 0^n 1^n | n >= 0
- This is correct. As explained above, the grammar generates this language.
- Option c: 0^n 1^n | n >= 1
- This is incorrect because it excludes the empty string. The grammar allows n to be 0, making this option false.
- Option d: None of the mentioned
- This is correct because the only incorrect statement is option c.
Conclusion
Thus, option d is indeed the correct answer, as it acknowledges that the statements regarding the language produced by the grammar are valid, except for option c. The language is non-regular and includes the empty string.
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For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer?.
For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For S->0S1|e for ∑={0,1}*, which of the following is wrong for the language produced?a)Non regular languageb)0n1n | n > = 0c)0n1n | n > = 1d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer?.
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