A student wants to determine whether a certain problem is undecidable. Which of the following will demonstrate that the problem is undecidable? Show that for one instance of the problem an algorithm can be written that is always capable of providing a correct yes-or-no answer. B Show that for one instance of the problem no algorithm can be written that is capable of providing a correct yes-or-no answer. C Show that for one instance of the problem a heuristic is needed to write an algorithm that is capable of providing a correct yes-or-no answer. D Show that for one instance of the problem an algorithm that runs in unreasonable time can be written that is capable of providing a correct yes-or-no answer

Question

A student wants to determine whether a certain problem is undecidable. Which of the following will demonstrate that the problem is undecidable? Show that for one instance of the problem an algorithm can be written that is always capable of providing a correct yes-or-no answer. B Show that for one instance of the problem no algorithm can be written that is capable of providing a correct yes-or-no answer. C Show that for one instance of the problem a heuristic is needed to write an algorithm that is capable of providing a correct yes-or-no answer. D Show that for one instance of the problem an algorithm that runs in unreasonable time can be written that is capable of providing a correct yes-or-no answer

Answer 1

The correct answer is B. To demonstrate that a problem is undecidable, it is necessary to show that no algorithm can be written that is capable of providing a correct yes-or-no answer for at least one instance of the problem. This means that there is no definitive method or procedure that can be followed to determine whether a given instance of the problem has a solution or not. In other words, the problem is undecidable if it is impossible to design an algorithm that can accurately determine the answer for all possible instances of the problem.

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