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Questions about decision problems that can be solved on nondeterministic Turing machines in time polynomial in the length of the input.
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The meaning of Tautology and Contradiction in Complexity theory
I recently had this question answered on stack exchange:
if X is in NP but Y is not in NP then can X be reduced to Y? … $ that could be reduced to any other problem, including those not in $NP$, thereby giving a direct counter example to the statement: $X \in NP \land Y \not\in NP \implies X \not\le^m_p Y$
What interests …
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if X is in NP but Y is not in NP then can X be reduced to Y?
Since X is in NP there must exist some NP-complete problem Z that it reduces to and my thinking is that any other problem that X reduces to must also reduce to this NP-complete problem Z, that is, since … X is in NP both it and any problem it can be reduced to must also reduce to an NP-complete problem Z so it cannot be the case that X can be reduced to a problem Y that is NOT in NP. …