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Exact derandomization of logarithmic space: L = RL = BPL

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OpenAI Mathopenai-math/Exact-Derandomization-of-Logarithmic-Space-L-equals-RL-equals-BPLSep 23, 2026cs.CCAI-generatedscore 0 · 🔥 1 post

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

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The MathocalypseShtetl-OptimizedOct 7, 2026

Though its truth was never in serious doubt, there was a whole subcommunity focused on proving this. The Fourier Transform and integer multiplication in less than O(n log n) time, breaking a barrier that had stood since the 1960s. The new running time, if you’re curious, is O(n log 0.9999999999999…

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