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This isn't my area, so many apologies if I say something incorrect: 1) "What evidence do we have that $\mathsf{BPP}\subseteq \mathsf{REXP}$?" Isn't this unconditionally true? It should follow from $\mathsf{BPP}\subseteq \mathsf{EXP}$, and in fact by Sipser-Gács-Lautemann $\mathsf{BPP}\subseteq \Sigma^p_2\cap \Pi_2^p$. 2) "What consequences does $\mathsf{...

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