Discussion
Which methods can establish that a problem has no solution?
Answer: C
Only a method that exhausts the space, or derives a contradiction, can assert absence, and the incomplete methods can never do so however long they run. That is not a matter of time. The stochastic methods sample and cannot exhaust. Knowing which family a task requires, before selecting an algorithm within it, is a decision that follows directly from what must be concluded at the end.
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