Author

K. Balodis

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Preprint Aug 2026

An Optimal Separation Between Certificate Complexity and Approximate Degree

We prove that certificate complexity can be quartically larger than approximate degree. More precisely, we construct a family of total Boolean functions $G$ with $$ C(G) = \tilde{\Omega}(\tilde{deg}(G)^4), $$ where $C$ denotes certificate complexity and $\tilde{deg}$ denotes $1/3$-approximate degree. This is optimal up...

K. Balodis · 2 citations · ⚡1