OpenAI and Anthropic Models Challenge the Exponential Time Hypothesis

OpenAI and Anthropic say algorithms developed by their models refute the Exponential Time Hypothesis (ETH), a long-standing assumption about how quickly computers can solve certain problems. The claims have prompted computer scientists to examine the proofs and what they could mean for the field.

MIT computer scientist Ryan Williams is helping organize that response. He and UC San Diego researchers Russell Impagliazzo and Ramamohan Paturi, who first published ETH in 1999, released an open letter seeking scientific feedback and discussion of norms for AI contributions. Williams told TechCrunch that parts of OpenAI’s proof looked routine, while two or three sections looked unusual enough to merit work by the broader community.

ETH says that, for a particular class of difficult logic puzzles, even the fastest algorithms need exponentially more time as the number of variables grows. OpenAI and Anthropic claim their models found algorithms that solve such puzzles in sub-exponential time. If the results hold up, they could challenge ETH and affect research that has relied on it. They do not, by themselves, establish that P = NP.

Williams said OpenAI checked whether the result affected cryptographic systems and was reasonably confident it did not imply any breaks. He also said the algorithms may not be the best possible. Computer scientists are now discussing how to review the work and reassess assumptions built on ETH.