Exact derandomization of logarithmic space: L = RL = BPL
Source: github.com/openai/math/tree/main/preprints/Exact-Derandomiz…
We prove $\mathsf L=\mathsf{RL}=\mathsf{BPL}$, resolving the derandomization problem for polynomial-time randomized logarithmic space.
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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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Open No Moreblog.computationalcomplexity.orgLance Fortnow
A full derandomization of randomized log space Matrix multiplication in \(n^{2.25+\epsilon}\) time (formalized in Lean) And many many more. I had Claude put together a webpage to make it easier to explore the TCS-related results. Now these proofs haven't been fully verified but if they hold up,…