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One possible direction is looking at the (computational) hardness of distributions. For example, a family of distributions $\{\mathcal{P}_n\}_{n\in\mathbb{N}}$ where $\mathcal{P}_n$ is a distribution over $\{0,1\}^n$ is called polynomialy-samplable (you can substitute here any other type of time/space restriction) if there exists a probabilistic polynomial ...


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