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Which term describes a problem that is at least as hard as the hardest problems in NP?

NP-Complete

NP-Hard

The term that describes a problem that is at least as hard as the hardest problems in NP is NP-Hard. To understand this, it is essential to grasp the relationship between the classes of problems in computational complexity.

NP-Hard problems are those for which, even though they may not necessarily belong to the NP class themselves, every problem in NP can be transformed into them in polynomial time. This indicates that NP-Hard problems are at least as challenging as the most difficult problems in NP, meaning that if you could solve an NP-Hard problem efficiently, you could also solve all NP problems efficiently.

In contrast, NP-Complete problems are a specific subset of NP problems that are both in NP and NP-Hard. Therefore, while NP-Complete problems pose significant challenges, NP-Hard encompasses an even broader group of problems that includes those not confined to the NP category.

The classes P and Polynomial do not adequately describe the complexity stemming from NP, as P refers to problems that can be solved in polynomial time and does not capture the hardness aspect associated with NP-Hard or NP-Complete classifications. Thus, NP-Hard captures the essence of the question accurately.

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P

Polynomial

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