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Results tagged with reductions
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A reduction is the transformation of one problem into another problem. A example of using a reduction would be to be to show if a problem P is undecidable. This would be achieved by transforming or performing a reduction of a decision problem $P$ into an undecidable problem. If this can be achieved then we have shown that this problem P is undecidable.
20
votes
Accepted
Nontrivial membership in NP
Integer Programming.
Showing that if there is an integer solution then there is a polynomial size integer solution is quite involved. See
Christos Papadimitriou, "On the Complexity of Integer Prog …
- 21.8k
15
votes
Accepted
Does NP-completeness/hardness have to be constructive?
Yes, there are such sets, take any $\mathsf{NP}$-intermediate set (any set that is provably $\mathsf{NP}$-intermediate assuming $\mathsf{P}\neq\mathsf{NP}$), e.g. construct one from SAT using Ladner's …
- 21.8k
9
votes
Should reductions make us more or less optimistic for the tractability of a problem?
However, although they are technically reductions
we often don't refer to these as such.
What we mean by a reduction is usually a reduction to some (NP-)hard problem. … If you accept these conjectures then
it is completely reasonable to look at reductions proving
universality of a problem for NP as the problem being hard. …
- 21.8k
10
votes
Advanced techniques for determining complexity lower bounds
The techniques depend on the model and the type of resource
we want to get a lower bound on.
Note that to prove a lower bound on the complexity of a problem
we have to first fix a mathematical model o …
- 21.8k