are all problems in P in NP

Asked Aug 21 '20 at 12:27

Active Aug 21 '20 at 12:27

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I know this is a similar question to this post, but I want to further clarify my understanding. In the picture from wikipedia:

I understand that every problem that's in $P$ is also in NP. does this mean that everything from MergeSort, to linear search is in NP [though not NP-HARD]? Or does this only apply to decision problems [aka YES, NO].

But then is it possible to turn any problem that is solvable in less than exponential time into a problem in $P$, hence a problem in $NP$?

thanks!

asked Aug 21 '20 at 12:27

Katie Melosto

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Our reference question on P and NP provides a basic, but thorough introduction to the topic, which includes an answer to the question in your title. – Discrete lizard Aug 21 '20 at 12:33
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As for your final question, note that "less than exponential" can still be "more than polynomial" (although it depends a bit on the precise definitions involved) – Discrete lizard Aug 21 '20 at 12:35
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Thanks @Discretelizard, That's helpful and I see in your link that P is a subset of NP – Katie Melosto Aug 21 '20 at 12:36

are all problems in P in NP

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