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Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A* to B* .We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let Lf denotes the language {x#f(x)|x∈A*}. Which of the following statements is true?
  • a)
    f if computable if and only if Lf is recursive.
  • b)
    f if computable if and only if Lf is recursive enumerable.
  • c)
    if f is computable then Lf is recursive, but not conversely.
  • d)
    if f is computable then Lf is recursively enumerable, but not conversely.
Correct answer is option 'A'. Can you explain this answer?
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Let A and B be infinite alphabets and let # be a symbol outside both A...
This definition is given as Halting of Turing Machine. Every recursive language is computable, but converse may not be true.
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Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A*to B*.We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let Lfdenotes the language {x#f(x)|x∈A*}. Which of the following statements is true?a)f if computable if and only if Lfis recursive.b)f if computable if and only if Lfis recursive enumerable.c)if f is computable then Lfis recursive, but not conversely.d)if f is computable then Lfis recursively enumerable, but not conversely.Correct answer is option 'A'. Can you explain this answer?
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Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A*to B*.We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let Lfdenotes the language {x#f(x)|x∈A*}. Which of the following statements is true?a)f if computable if and only if Lfis recursive.b)f if computable if and only if Lfis recursive enumerable.c)if f is computable then Lfis recursive, but not conversely.d)if f is computable then Lfis recursively enumerable, but not conversely.Correct answer is option 'A'. 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 Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A*to B*.We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let Lfdenotes the language {x#f(x)|x∈A*}. Which of the following statements is true?a)f if computable if and only if Lfis recursive.b)f if computable if and only if Lfis recursive enumerable.c)if f is computable then Lfis recursive, but not conversely.d)if f is computable then Lfis recursively enumerable, but not conversely.Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let A and B be infinite alphabets and let # be a symbol outside both A and B. Let f be a total functional from A*to B*.We say f is computable if there exists a Turning machine M which given an input x in A*, always halts with f(x) on its tape. Let Lfdenotes the language {x#f(x)|x∈A*}. Which of the following statements is true?a)f if computable if and only if Lfis recursive.b)f if computable if and only if Lfis recursive enumerable.c)if f is computable then Lfis recursive, but not conversely.d)if f is computable then Lfis recursively enumerable, but not conversely.Correct answer is option 'A'. Can you explain this answer?.
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