Is NP-Complete Harder to Solve than NP-Hard?

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NP-Complete problems are a subset of NP-Hard problems, meaning all NP-Complete problems are NP-Hard, but not all NP-Hard problems are NP-Complete. NP-Complete problems can be solved in polynomial time if a solution exists, while NP-Hard problems may not even be solvable in polynomial time and include problems like the halting problem. The distinction lies in the fact that NP-Hard problems that are not NP-Complete require more computational resources and can be more complex. Therefore, NP-Hard problems are generally considered harder than NP-Complete problems due to their broader scope and potential unsolvability. This discussion highlights the nuances in classifying problem difficulty within computational theory.
jetoso
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I have a question. Is the class of problems NP-Complete more difficult to solve than the class of problems NP-Hard?

I mean, NP-Complete problems are in NP, and also are NP-Hard, but not all NP-Hard problems are in NP... How to tell which one is more difficult to solve?
 
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The set of problems that are NP-hard is a strict superset of the problems that are NP-complete. Some problems (like the halting problem) are NP-hard, but not in NP.
 
NP-Hard problems that are not NP-Complete are 'harder' than NP problems, in general, in that they take up more computational resources of some type: memory, time, alternation, randomness, etc.
 
Or as Nate mentioned, NP-hard problems might be impossible to solve in general. You can tell the difference in difficulty between NP-hard and NP-complete problems because the class NP includes everything easier than its "toughest" problems--if a problem is not in NP, it is harder than all the problems in NP.

By the way, would you post things like this in the future in the Programming forum, as it is a computer science question?
 
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