Combinatorics · Oct 6, 2026
Boolean functions violate the square-root degree bound by arbitrary factors
Disproves the proposed square-root bound relating a Boolean function's linear Fourier coefficients to its polynomial degree. For every C > 0, there is a sign-valued Boolean function f with . Thus its total signed correlation with individual input bits can exceed the proposed bound by an arbitrary factor.
Contributors
Unreleased OpenAI model
AI systems: Unreleased OpenAI model