Theoretical computer science·OpenAI Math·Result 103·Lean formalisation listed
Exact derandomization of logarithmic space: L=RL=BPL
One of the 372 results in OpenAI's public mathematics catalogue, filed under theoretical computer science: 1 preprint, the latest dated 23 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and embeds the animation.
Also known as L = RL = BPL; derandomization of logarithmic space
In one line: OpenAI reports a result titled ‘Exact derandomization of logarithmic space: L=RL=BPL’ (theoretical computer science) in a preprint dated 23 September 2026. It has not been peer reviewed. The channel's animation, Every OpenAI Math Result, Part 4 of 4: L = BPL, Integer Multiplication and 82 More, is on YouTube.
Chapter 7 of 84 in Every OpenAI Math Result, Part 4 of 4: L = BPL, Integer Multiplication and 82 More · starts at 2:05 · watch from there on YouTube →
What OpenAI claims
Proves L=RL=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. (Lean)
Paper
Exact derandomization of logarithmic space: L = RL = BPL
OpenAI's abstract We prove L=RL=BPL, resolving the derandomization problem for polynomial-time randomized logarithmic space.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
Quick answers
- Is it proven?
- Not independently yet. OpenAI posted a preprint on 23 September 2026; it has not been peer reviewed, so treat the result as OpenAI's claim until other mathematicians have checked it.
- What exactly does OpenAI claim?
- Proves L=RL=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. (Lean)
- Where is the proof?
- In the paper, Exact derandomization of logarithmic space: L = RL = BPL (PDF).
- Is there a video?
- Yes, on YouTube (29:10, chapter 7).
Also in
- Chapter 5 of 9 in L = BPL, Matrix Multiplication Exponent, Integer Multiplication and 6 More · starts at 1:23 · watch from there on YouTube →
The video
Every OpenAI Math Result, Part 4 of 4: L = BPL, Integer Multiplication and 82 More · Compilation · 29:10 · chapter 7 from 2:05 · description, sources and chapters →
Related results in Theoretical computer science
- 104Quasipolynomial algorithms for mean-payoff, stochastic and parity gamesLean
- 105Perfect completeness for 2-to-1 gamesVideoLean
- 106Hardness of coloring three-colorable graphsVideoLean
- 107Matrix multiplication with exponent at most 9/4VideoLean
- 108A cubic permanent–determinant lower boundVideoLean
- 109Integer multiplication below n log nVideo
