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A percentage point or percent point is the unit for the arithmetic difference between two percentages.For example, moving up from 40 percent to 44 percent is an increase of 4 percentage points (although it is a 10-percent increase in the quantity being measured, if the total amount remains the same). [1]
Surprisingly, some #P problems that are believed to be difficult correspond to easy (for example linear-time) P problems. For more information on this, see #P-complete . The closest decision problem class to #P is PP , which asks whether a majority (more than half) of the computation paths accept.
As an example, if the two distributions do not overlap, say F is below G, then the P–P plot will move from left to right along the bottom of the square – as z moves through the support of F, the cdf of F goes from 0 to 1, while the cdf of G stays at 0 – and then moves up the right side of the square – the cdf of F is now 1, as all points of F lie below all points of G, and now the cdf ...
R vs. RE problem, where R is analog of class P, and RE is analog class NP. These classes are not equal, because undecidable but verifiable problems do exist, for example, Hilbert's tenth problem which is RE-complete. [57] A similar problem exists in the theory of algebraic complexity: VP vs. VNP problem. This problem has not been solved yet.
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As a result, P = NP leads to P = BPP since PH collapses to P in this case. Thus either P = BPP or P ≠ NP or both. Adleman's theorem states that membership in any language in BPP can be determined by a family of polynomial-size Boolean circuits , which means BPP is contained in P/poly . [ 5 ]
A polynomial time Turing machine with a PP oracle (P PP) can solve all problems in PH, the entire polynomial hierarchy. This result was shown by Seinosuke Toda in 1989 and is known as Toda's theorem. This is evidence of how hard it is to solve problems in PP. The class #P is in some sense about as hard, since P #P = P PP and therefore P #P ...
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