Rational degree is polynomially related to degree

Robin Kothari; Matt Kovacs-Deak; Daochen Wang; Rain Zimin Yang

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arXiv · 2601.08727

Rational degree is polynomially related to degree

Robin Kothari·Matt Kovacs-Deak·Daochen Wang·Rain Zimin Yang

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Abstract

We prove that $\mathrm{deg}(f) \leq \widetilde{O}(\mathrm{rdeg}(f)^3)$ for every Boolean function $f$, where $\mathrm{deg}(f)$ is the degree of $f$ and $\mathrm{rdeg}(f)$ is the rational degree of $f$. This resolves the second of the three open problems stated by Nisan and Szegedy, and attributed to Fortnow, in 1994.

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Robin Kothari, Matt Kovacs-Deak, Daochen Wang, Rain Zimin Yang. 2026-01-13. Rational degree is polynomially related to degree. https://arxiv.org/abs/2601.08727

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