Derandomization of logarithmic space: is L = RL = BPL?

Claims $\mathsf L=\mathsf{RL}=\mathsf{BPL}$: every language decided with bounded one-sided or two-sided error by a randomized machine with polynomial worst-case running time and $O(\log n)$ space is decided by a deterministic $O(\log n)$-space machine. Quantitatively, acceptance probabilities can be approximated to within $2^{-q}$ in space $O(\log(n+2)+q)$ and time $(n+2)^{O(1)}2^{O(q)}$. The method builds a hierarchy of copies of the configuration graph with a shared finite random environment and evaluates a family of $O(\log n)$-bit estimators, more than three quarters of them accurate, by exhaustive enumeration. It does not give a pseudorandom generator with logarithmic seed, and it does not address randomized logspace without a polynomial time bound.

Claims $\mathsf L=\mathsf{RL}=\mathsf{BPL}$: every language decided with bounded one-sided or two-sided error by a randomized machine with polynomial worst-case running time and $O(\log n)$ space is decided by a deterministic $O(\log n)$-space machine. Quantitatively, acceptance probabilities can be approximated to within $2^{-q}$ in space $O(\log(n+2)+q)$ and time $(n+2)^{O(1)}2^{O(q)}$. The method builds a hierarchy of copies of the configuration graph with a shared finite random environment and evaluates a family of $O(\log n)$-bit estimators, more than three quarters of them accurate, by exhaustive enumeration. It does not give a pseudorandom generator with logarithmic seed, and it does not address randomized logspace without a polynomial time bound.