New OpenAI paper claims the Exponential Time Hypothesis (ETH) is false
OpenAI has released a new paper claiming to give a deterministic subexponential-time algorithm that can exactly count the solutions to k-SAT; if the proof holds, it would overturn the Exponential Time Hypothesis (ETH). The paper bluntly titles itself "The Exponential Time Hypothesis Is False"; ETH is one of the core assumptions of modern fine-grained complexity theory and has long been used to argue that a large family of problems may not be substantially sped up. If the proof holds, a large number of conditional lower bounds built on ETH and SETH will need to be re-examined. The paper also claims this result has implications for problems such as #SAT, graph coloring, independent set, and perfect matching.
If OpenAI's claimed subexponential algorithm is proven to hold, a large number of conditional lower bounds based on ETH and SETH will need to be re-examined.
The Exponential Time Hypothesis Is False!
OpenAI just shook one of the foundations of computer science.
In a new paper bluntly titled “The Exponential Time Hypothesis Is False,” OpenAI claims a deterministic, subexponential-time algorithm for exactly counting solutions to k-SAT — which would refute ETH, one of the central assumptions underpinning modern fine-grained complexity theory.
ETH has long been used to argue that huge families of problems probably cannot be solved substantially faster. If this proof holds, a large body of conditional lower bounds built on ETH and SETH will need to be re-examined.
The paper also claims consequences for #SAT, graph coloring, independent sets, perfect matchings, and more.