Which of the following is true about the Halting Problem?

Options

  • A. It can be solved in O(1) time
  • B. It can be solved in polynomial time for all programs
  • C. No general algorithm exists that correctly determines halting for every program and input
  • D. More than one of the above
  • E. None of the above

Correct Answer (Detailed Explanation is Below)

C. No general algorithm exists that correctly determines halting for every program and input

Detailed Explanation

  • Undecidability: The general Halting Problem is mathematically proven to be undecidable.
  • No Universal Solver: There is no algorithm that correctly predicts halting for every possible program and input.
  • Important: Some restricted classes of programs can have decidable halting analysis.
  • Exam Point: Undecidability is stronger than simply having a very high time complexity.
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TRE 4 Theory of computations Practice set 1

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