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In computational complexity, NP is the complexity class consisting of problems whose yes instances can be verified in polynomial time. NP stands for 'nondeterministic polynomial time '.

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Constructing hard inputs for the complement of bounded halting

No, such $\langle N', x'\rangle$ is not constructible at all given only a description of $M$, even if you remove the requirement of polynomial time. Suppose that $CONSTRUCT$ is such a deterministic t …
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