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I think the best way to explain my question would be to have sextuple (regular, context-free, Turing-recognisable, decidable, P, NP).were you fill out 1 for promblem which lies into that section, would an np problem such as chess be only 1 for NP or would also fall in decidable?

Some other examples: The regular problem would be (1,1,1,1,1,1) as regular is a subset of CF,TR, Decidable which runs in P time and NP is a subset of NP.

Another example, a context-free language would be (0,1,1,1,1,1).

and I assume chess would be (0,0,1,1,0,1)

So my question is would my assumption on NP problems be correct as some decider has to recognize them?

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  • $\begingroup$ Chess is not an NP problem, in the sense it is not within the complexity class NP. It's an NP-hard problem. $\endgroup$
    – rus9384
    May 17, 2023 at 18:28

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Yes, this is correct, due to the computational equivalence of nondeterministic turing machines to deterministic ones. You can try all possible certificates in exponential time.

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