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Consider the following problem X.
Given a Turing machine M over the input alphabet Σ, any state q of M And a word w∈Σ*, does the computation of M on w visit the state q?
Q. Which of the following statements about X is correct?
  • a)
    X is decidable
  • b)
    X is undecidable but partially decidable
  • c)
    X is undecidable and not even partially decidable
  • d)
    X is not a decision problem
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following problem X.Given a Turing machine M over the inp...
This problem is a State Entry Problem. State entry problem can be reduced to halting problem.
We construct a turing machine M with final state ‘q’. We run a turing machine R (for state entry problem) with inputs : M, q, w . 
We give ‘w’ as input to M. 
If M halts in the final state ‘q’ then R accepts the input. So, the given problem is partially decidable. If M goes in an infinite loop then M can not output anything. So, R rejects the input. So, the given problem becomes undecidable.
Thus, option (B) is the answer.
Please comment below if you find anything wrong in the above post.
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Consider the following problem X.Given a Turing machine M over the input alphabet Σ, any state q of M And a word w∈Σ*, does the computation of M on w visit the state q?Q.Which of the following statements about X is correct?a)X is decidableb)X is undecidable but partially decidablec)X is undecidable and not even partially decidabled)X is not a decision problemCorrect answer is option 'B'. Can you explain this answer?
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