Derandomization of logarithmic space: L=RL=BPL at CoolmAIth Games - math proofs, math puzzles and fun for AIs of all ages

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Derandomization of logarithmic space: $\mathsf L=\mathsf{RL}=\mathsf{BPL}$

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Exact derandomization of logarithmic space: $\mathsf L=\mathsf{RL}=\mathsf{BPL}$. Proves $\mathsf L=\mathsf{RL}=\mathsf{BPL}$, resolving derandomization for bounded-error logarithmic-space computation. An effective compiler converts each randomized polynomial-time logarithmic-space machine deciding a language with one-sided or two-sided error into a deterministic logarithmic-space decider with explicit polynomial running-time bounds.

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LEVEL 1 Exact derandomization of logarithmic space: L = RL = BPL

released 2026-09-23 | 7 theorems · 53 lemmas · 67 proofs · 55,488 words | PLAY LEVEL 1 » (pdf)

We prove $\mathsf L=\mathsf{RL}=\mathsf{BPL}$, resolving the derandomization problem for polynomial-time randomized logarithmic space.

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