Adleman showed that $\mathsf{BPP/poly} \subseteq \mathsf{P/poly}$. Does $\mathsf{P} = \mathsf{BPP}$ have any implications for
- $\mathsf{BPP}/a(n) \subseteq \mathsf{P}/a(n)$
- $\mathsf{BPTIME}(t(n))/a(n) \subseteq \mathsf{DTIME}(t'(n))/a'(n)$
where $a(n)$ and $a'(n)$ are some fixed functions, e.g. $a(n) = \log_2(n)$ or even $a(n) = 1$, and $t(n)$ and $t'(n)$ are some time-bound?
Note: If $a'(n) \geq t(n) + a(n)$, then a deterministic TM $\mathcal{A}$ can include as advice the $a(n)$-bit randomness of a randomized TM $\mathcal{R}$ plus $\mathcal{R}$'s $t(n)$-bit advice.