Question

What is the significance of the ‘halting problem’ in computability theory?

• A. It proves that all algorithms can be optimized
• B. It shows that some problems cannot be solved by any algorithm
• C. It demonstrates the efficiency of recursive algorithms
• D. It establishes the need for parallel computing

Hint:

The halting problem shows that some problems are undecidable, meaning there is no algorithm that can determine if a program will halt.

Answer 1

The Correct Option is B

The halting problem, first introduced by Alan Turing, is a fundamental concept in computability theory. It proves that there is no general algorithm that can decide whether an arbitrary program will halt (finish) or run forever for a given input. This result shows that some problems are undecidable, meaning no algorithm can solve them in all cases.
- It proves that all algorithms can be optimized (A) is incorrect, as the halting problem does not address algorithm optimization.
- It demonstrates the efficiency of recursive algorithms (C) is unrelated to the halting problem, which focuses on undecidability rather than efficiency.
- It establishes the need for parallel computing (D) is not a focus of the halting problem, which is concerned with the limits of computation.
Therefore, the correct answer is (B).