Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following set of statements:S1:G...
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Consider the following set of statements:
S1: Given a context-free language, there is a Turing machine which will always halt in the finite amount of time and give answer whether language is ambiguous or not.
S2: Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.
S3: Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable. P3 is undecidable if P2 is reducible to P3.
Which of the given statements is true?
- a)Both S1 and S2
- b)Both S2 and S3
- c)Only S1
- d)Both S1 and S3
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following set of statements:S1:Given a context-free langu...
Statements S2 and S3 are true.
Statement S1 can be corrected as: Given a context-free language, there is no Turing machine which will always halt in the finite amount of time and give answer whether language is ambiguous or not.
Most Upvoted Answer
Consider the following set of statements:S1:Given a context-free langu...
Analysis of Statements
The given statements relate to concepts in formal languages and computability. Let's break down each statement to understand their validity.
Statement S1
- Ambiguity of Context-Free Languages: This statement claims that there exists a Turing machine that can always decide whether a given context-free language (CFL) is ambiguous.
- Truth of S1: This statement is false. The ambiguity of CFLs is undecidable. There is no algorithm that will always halt and provide an answer to whether a given CFG is ambiguous.
Statement S2
- CFG and Language Generation: This statement posits that it is undecidable to determine whether a given context-free grammar (CFG) generates all possible strings over its input alphabet (Σ*).
- Truth of S2: This statement is true. It is known that the problem of whether a CFG generates all strings over its alphabet is undecidable.
Statement S3
- Reduction and Undecidability: This statement is about decision problems, stating that if P2 is undecidable, then P3 is also undecidable if P2 can be reduced to P3.
- Truth of S3: This statement is true. If there is a reduction from an undecidable problem (P2) to another problem (P3), then P3 must also be undecidable.
Conclusion
- Correct Answer: Since S2 and S3 are true while S1 is false, the correct answer is indeed option B: Both S2 and S3 are true.
The given statements relate to concepts in formal languages and computability. Let's break down each statement to understand their validity.
Statement S1
- Ambiguity of Context-Free Languages: This statement claims that there exists a Turing machine that can always decide whether a given context-free language (CFL) is ambiguous.
- Truth of S1: This statement is false. The ambiguity of CFLs is undecidable. There is no algorithm that will always halt and provide an answer to whether a given CFG is ambiguous.
Statement S2
- CFG and Language Generation: This statement posits that it is undecidable to determine whether a given context-free grammar (CFG) generates all possible strings over its input alphabet (Σ*).
- Truth of S2: This statement is true. It is known that the problem of whether a CFG generates all strings over its alphabet is undecidable.
Statement S3
- Reduction and Undecidability: This statement is about decision problems, stating that if P2 is undecidable, then P3 is also undecidable if P2 can be reduced to P3.
- Truth of S3: This statement is true. If there is a reduction from an undecidable problem (P2) to another problem (P3), then P3 must also be undecidable.
Conclusion
- Correct Answer: Since S2 and S3 are true while S1 is false, the correct answer is indeed option B: Both S2 and S3 are true.
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Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. 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 Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. 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 Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. Can you explain this answer?.
Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. 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 Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. 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 Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. Can you explain this answer?.
Solutions for Consider the following set of statements:S1:Given a context-free language, there is a Turing machine which will always halt in thefinite amount of time and give answer whether language is ambiguous or not.S2:Given a CFG and input alphabet, whether CFG will generate all possible strings of input alphabet (∑*) is undecidable.S3:Consider three decision problems P1, P2 and P3. It is known that P1 is decidable and P2 is undecidable.P3 is undecidable if P2 is reducible to P3.Which of the given statements is true?a)Both S1 and S2b)Both S2 and S3c)Only S1d)Both S1 and S3Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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