https://github.com/openai/math/tree/main/preprints/The-Expon...
>We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula [in superpolynomial but subexponential time]
https://github.com/openai/math/tree/main/preprints/The-Expon...
>We give a deterministic algorithm for exactly counting the satisfying assignments of an arbitrary k-CNF formula [in superpolynomial but subexponential time]
I assumed all new breakthroughs in advanced complexity theory would be theoretical and non-constructive, as in "we prove that this algorithm must exist but we do not provide it".
I'm genuinely shook at today's results, specially at the fact that there _is_ a constructive algorithm.
What a time to be alive honestly. Can’t know what one will wake up to
> superpolynomial
I've got some reading to do it seems...
Polynomial is something like exp(n log x), where x is the problem size. Exponential is something like exp(x). Superpolynomial but subexponential is roughly when the exponent is between n log x and x. An exponent of (log x)^2 would do the trick.
The actual exponent OpenAI found was x/sqrt(x).