Artificial Intelligence Programming Practice Exam

Intractable problems are best characterized as those that are solvable in theory but impractical to solve in reality. This means that while there exists a theoretical algorithm that could solve the problem, the time and resources required to execute that solution become infeasible as the size of the input or the complexity of the problem increases.

For example, many problems fall under the category of NP-hard problems, which means that no known polynomial-time algorithm can efficiently solve them for large input sizes. In practice, this indicates that for reasonable inputs, the computational resources—such as time and memory—needed to find a solution could grow exponentially, rendering the problem intractable for practical purposes.

This definition is distinct from the other choices, which do not accurately capture the essence of intractable problems. Problems with no solutions would imply that they are unsolvable, which does not encompass the theoretical solvability of intractable problems. Similarly, problems that are easy to solve would indicate the opposite of intractability. Lastly, while it is true that intractable problems often require extensive resources, this is not a defining characteristic, as not all problems requiring substantial resources are necessarily intractable; they may simply be challenging but still solvable in a reasonable timeframe.