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Question

Consider the following Problem X.
"Given a Turing machine M over the input alphabet . any state q of M and a word , does the computation of M on w visit the state q"
Which of the following statements about X is correct?

A
X is not a decision problem
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B
X is decidable
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C
X is undecidable but partially decidable
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D
X is undecidable and not even partially decidable
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Solution

The correct option is C X is undecidable but partially decidable
Problem X is state entry problem. Halting problem of turing machine can be reduced to state entry problem. Since halting problem of turing machine is undecidable. the state-entry problem must also be undecidable. The language corresponding to state-entry problem is RE but not REC. So X is undecidable but partially decidable.

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