#p-complete Conditional Distributions
نویسندگان
چکیده
We study conditional probability from the perspective of complexity theory of functions and operators in analysis, building on work by Ko (1983), Friedman (1984), and Kawamura and Cook (2010). For some random variable X in {0, 1}N whose distribution is continuous and polynomial-time computable, and some polynomial-time computable function f : {0, 1}N → [0, 1] for which the random variable f(X) is “polynomially-diffuse”, the function taking (integers encoding) A ∈ {0, 1}∗, an open rational interval B, and an accuracy 2−i to a rational within 2−i of the conditional probability that X ∈ A given f(X) ∈ B is shown to be #P-complete. On the other hand, all such functions computing conditional probabilities are in #P.
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