OpenAI Claims Exponential Time Hypothesis Is False

OpenAI’s Exponential Time Hypothesis Claim

Two of the computer scientists who proposed the Exponential Time Hypothesis in the late 1990s must now decide whether a machine has broken it. OpenAI said on Monday that an internal model refuted the conjecture, and Russell Impagliazzo and Ramamohan Paturi will lead an independent review of the claim with MIT’s Ryan Williams.

Key Takeaways

• OpenAI says an internal model found a disproof of the Exponential Time Hypothesis on October 16 and checked it in Lean a day later, then posted the paper and proof on GitHub.
• The company also claims proofs of the local smoothing conjecture in all dimensions, which would settle Kakeya and Stein restriction, and of four-dimensional Yang-Mills and QCD existence.
• The reviewers say their role does not certify the result, and a physics group led by Nobel laureate David Gross is holding back the Yang-Mills material for now.

What the Model Claims

The hypothesis concerns Boolean satisfiability, a problem closely tied to P versus NP. It holds that 3-SAT cannot be solved in subexponential time. Researchers have relied on it to argue that problems in graph theory, computational biology and databases resist fast solutions.