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Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1 and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?
- a)Only I and II are undecidable
- b)Only II is undecidable
- c)Only II and IV are undecidable
- d)Only I, II and III are undecidable
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Consider the following problems. L(G) denotes the language generated b...
I, II and III are undecidable, refer this:
Coming to IV, every regular language is Deterministic-CFL, which is a trivial property. Option (D) is Correct.
Coming to IV, every regular language is Deterministic-CFL, which is a trivial property. Option (D) is Correct.
Most Upvoted Answer
Consider the following problems. L(G) denotes the language generated b...
Understanding the Problems
The problems presented involve various types of grammars and machines in the context of formal languages and automata theory. Let's evaluate each one for decidability.
Problem I: Unrestricted Grammar Membership
- Description: For an unrestricted grammar G, determine whether a string w belongs to L(G).
- Decidability: This problem is undecidable. It is equivalent to the problem of determining whether a Turing machine accepts a particular input.
Problem II: Turing Machine Language Regularity
- Description: Given a Turing machine M, determine whether L(M) is a regular language.
- Decidability: This problem is undecidable. There is no algorithm that can universally determine if the language accepted by an arbitrary Turing machine is regular.
Problem III: Language Equality of Two Grammars
- Description: Given two grammars G1 and G2, check if L(G1) = L(G2).
- Decidability: This problem is undecidable. There is no general procedure to determine if two arbitrary context-free grammars generate the same language.
Problem IV: NFA and PDA Language Equivalence
- Description: Given a non-deterministic finite automaton (NFA) N, determine if there exists a deterministic pushdown automaton (PDA) P such that N and P accept the same language.
- Decidability: This problem is undecidable. There is no algorithm to establish the equivalence in language acceptance between an NFA and a deterministic PDA.
Conclusion
Based on the analysis, problems I, II, and III are all undecidable, confirming that option 'D' is indeed correct.
The problems presented involve various types of grammars and machines in the context of formal languages and automata theory. Let's evaluate each one for decidability.
Problem I: Unrestricted Grammar Membership
- Description: For an unrestricted grammar G, determine whether a string w belongs to L(G).
- Decidability: This problem is undecidable. It is equivalent to the problem of determining whether a Turing machine accepts a particular input.
Problem II: Turing Machine Language Regularity
- Description: Given a Turing machine M, determine whether L(M) is a regular language.
- Decidability: This problem is undecidable. There is no algorithm that can universally determine if the language accepted by an arbitrary Turing machine is regular.
Problem III: Language Equality of Two Grammars
- Description: Given two grammars G1 and G2, check if L(G1) = L(G2).
- Decidability: This problem is undecidable. There is no general procedure to determine if two arbitrary context-free grammars generate the same language.
Problem IV: NFA and PDA Language Equivalence
- Description: Given a non-deterministic finite automaton (NFA) N, determine if there exists a deterministic pushdown automaton (PDA) P such that N and P accept the same language.
- Decidability: This problem is undecidable. There is no algorithm to establish the equivalence in language acceptance between an NFA and a deterministic PDA.
Conclusion
Based on the analysis, problems I, II, and III are all undecidable, confirming that option 'D' is indeed correct.
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Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect answer is option 'D'. Can you explain this answer?
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Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect 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 Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect 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 Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect answer is option 'D'. Can you explain this answer?.
Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect 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 Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect 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 Consider the following problems. L(G) denotes the language generated by a grammar G. L(M) denotes the language accepted by a machine M. (I) For an unrestricted grammar G and a string w, whether wϵL(G) (II) Given a Turing machine M, whether L(M) is regular (III) Given two grammar G1and G2, whether L(G1) = L(G2) (IV) Given an NFA N, whether there is a deterministic PDA P such that N and P accept the same language Which one of the following statement is correct?a)Only I and II are undecidableb)Only II is undecidablec)Only II and IV are undecidabled)Only I, II and III are undecidableCorrect answer is option 'D'. Can you explain this answer?.
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