Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is incorrec...
Start Learning for Free
Which of the following statements is incorrect?
- a)Union of two DCFL is a CFL.
- b)Complementation of a regular language is a regular language.
- c)Turing recognizable languages are closed under intersection.
- d)None.
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Which of the following statements is incorrect?a)Union of two DCFL is ...
Statement 1 is correct because union of two DCFL may or may not be DCFL but surely CFL. Statement 2 is correct because regular languages are closed under complementation. Statement 3 is correct because Turing recognizable languages or recursive enumerable languages are closed under intersection.
Most Upvoted Answer
Which of the following statements is incorrect?a)Union of two DCFL is ...
Incorrect Statement: None (Option D)
Explanation:
- The incorrect statement is option D, which states that none of the statements are incorrect. However, this is not true as there are incorrect statements among the given options.
Analysis of each statement:
a) Union of two DCFL is a CFL:
- This statement is correct. The union of two deterministic context-free languages (DCFL) is a context-free language (CFL). This can be proven by constructing a context-free grammar or a pushdown automaton that recognizes the union of the two languages.
b) Complementation of a regular language is a regular language:
- This statement is correct. The complement of a regular language is also a regular language. This can be proven by constructing a deterministic finite automaton (DFA) for the original language and then flipping the accept and non-accept states to obtain a DFA for the complement language.
c) Turing recognizable languages are closed under intersection:
- This statement is incorrect. Turing recognizable (also known as recursively enumerable) languages are not closed under intersection. This means that the intersection of two Turing recognizable languages may not be Turing recognizable. This can be proven by showing a reduction from the halting problem to the intersection of two Turing recognizable languages.
Conclusion:
- The correct answer is option D, as it incorrectly states that none of the statements are incorrect. However, statement c) is incorrect as Turing recognizable languages are not closed under intersection.
Explanation:
- The incorrect statement is option D, which states that none of the statements are incorrect. However, this is not true as there are incorrect statements among the given options.
Analysis of each statement:
a) Union of two DCFL is a CFL:
- This statement is correct. The union of two deterministic context-free languages (DCFL) is a context-free language (CFL). This can be proven by constructing a context-free grammar or a pushdown automaton that recognizes the union of the two languages.
b) Complementation of a regular language is a regular language:
- This statement is correct. The complement of a regular language is also a regular language. This can be proven by constructing a deterministic finite automaton (DFA) for the original language and then flipping the accept and non-accept states to obtain a DFA for the complement language.
c) Turing recognizable languages are closed under intersection:
- This statement is incorrect. Turing recognizable (also known as recursively enumerable) languages are not closed under intersection. This means that the intersection of two Turing recognizable languages may not be Turing recognizable. This can be proven by showing a reduction from the halting problem to the intersection of two Turing recognizable languages.
Conclusion:
- The correct answer is option D, as it incorrectly states that none of the statements are incorrect. However, statement c) is incorrect as Turing recognizable languages are not closed under intersection.
Attention Computer Science Engineering (CSE) Students!
To make sure you are not studying endlessly, EduRev has designed Computer Science Engineering (CSE) study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Computer Science Engineering (CSE).
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer?
Question Description
Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 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 Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer?.
Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 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 Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer?.
Solutions for Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Which of the following statements is incorrect?a)Union of two DCFL is a CFL.b)Complementation of a regular language is a regular language.c)Turing recognizable languages are closed under intersection.d)None.Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup