I feel like there should be an easy example, but I can't think of one. So, specifically, I am looking for a Yes/No search problem that is not in the class NP. When you learn about P and NP, you get a lot of examples of problems in P, NP, NP-hard, NP-complete, co-NP, etc. I guess, halting problem would work, but I would like something for which computability is not the reason why it is not NP.
2026-03-27 03:41:12.1774582872
What is an example of a search problem that is not in NP?
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You can use the time hierarchy theorem to manufacture problems that have yes/no answers but which aren’t in NP by, say, requiring they take at least a super-polynomial amount of nondeterministic time to compute.
Another option is to look at NEXP-complete problems. The time hierarchy theorem guarantees that none of these problems are solvable in nondeterministic polynomial time, yet they’re all yes/no problems.