Matches in SemOpenAlex for { <https://semopenalex.org/work/W2794995312> ?p ?o ?g. }
- W2794995312 abstract "A simple way to generate a Boolean function is to take the sign of a real polynomial in $n$ variables. Such Boolean functions are called polynomial threshold functions. How many low-degree polynomial threshold functions are there? The partial case of this problem for degree $d=1$ was solved by Zuev in 1989, who showed that the number $T(n,1)$ of linear threshold functions satisfies $log_2 T(n,d) approx n^2$, up to smaller order terms. However the number of polynomial threshold functions for any higher degrees, including $d=2$, has remained open. We settle this problem for all fixed degrees $d ge1$, showing that $ log_2 T(n,d) approx n^{d+1}/{d!}$. The solution relies on establishing connections between the theory of Boolean functions and high-dimensional probability theory and leads to a more general program of extending random matrix theory to random tensors." @default.
- W2794995312 created "2018-04-06" @default.
- W2794995312 creator A5070281692 @default.
- W2794995312 creator A5088813478 @default.
- W2794995312 date "2018-03-28" @default.
- W2794995312 modified "2023-09-27" @default.
- W2794995312 title "Boolean polynomial threshold functions and random tensors" @default.
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