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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.
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Problems that are NP-complete under randomized or P/poly reductions.
In this question, we appear to have identified a natural problem that is NP-complete under randomized reductions, but possibly not under deterministic reductions (although this depends on which unproven … Are there any natural problems that are NP-complete under P/poly reductions, but not known to be under P reductions? …