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Research / Oct 6, 2026

Exact derandomization of logarithmic space: L = RL = BPL

Can the mathematical statement in Exact derandomization of logarithmic space: L = RL = BPL be proved and verified machine-checked in Lean?

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)
Oct 6, 2026

Lean formalization in OpenAI math repository (Result 103)

Model / AI: OpenAI (unreleased)

machine-checked (formal proof)self-reported (formal proof)

OpenAI's internal frontier model proved and formalized in Lean the main result of 'Exact derandomization of logarithmic space: L = RL = BPL'. We prove \mathsf L=\mathsf{RL}=\mathsf{BPL}, resolving the derandomization problem for polynomial-time randomized logarithmic space.

Source read 2026-10-08. Cataloged from OpenAI's formalization.yaml (Family 103). The Lean development was not rebuilt locally.