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That reduction function must be a computable function. In particular, we often show that a problem P is undecidable by showing that the halting problem reduces to P. The complexity classes P, NP and PSPACE are closed under (many-one, "Karp") polynomial-time reductions. The complexity classes L, NL, P, NP and PSPACE are closed under log-space ...
If a class is closed under many-one reducibility, then many-one reduction can be used to show that a problem is in C by reducing it to a problem in C. Many-one reductions are valuable because most well-studied complexity classes are closed under some type of many-one reducibility, including P , NP , L , NL , co-NP , PSPACE , EXP , and many others.
A closed-ended question is any question for which a researcher provides research participants with options from which to choose a response. [1] Closed-ended questions are sometimes phrased as a statement that requires a response. A closed-ended question contrasts with an open-ended question, which cannot easily be answered with specific ...
Viewing a decision problem as a formal language in some fixed encoding, the set NPC of all NP-complete problems is not closed under: union; intersection; concatenation; Kleene star [example needed] It is not known whether NPC is closed under complementation, since NPC=co-NPC if and only if NP=co-NP, and since NP=co-NP is an open question. [16]
In the computational complexity theory of counting problems, a polynomial-time counting reduction is a type of reduction (a transformation from one problem to another) used to define the notion of completeness for the complexity class ♯P. [1]
In computational complexity theory, a polynomial-time reduction is a method for solving one problem using another. One shows that if a hypothetical subroutine solving the second problem exists, then the first problem can be solved by transforming or reducing it to inputs for the second problem and calling the subroutine one or more times.
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A weak truth-table reduction is one where the reduction uses the oracle answers as a basis for further computation, which may depend on the given answers but may not ask further questions of the oracle. It is so named because it weakens the constraints placed on a truth-table reduction, and provides a weaker equivalence classification; as such ...