Supercritical Tradeoffs for Monotone Circuits

Mika Göös; Gilbert Maystre; Kilian Risse; Dmitry Sokolov

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arXiv · 2411.14268

Supercritical Tradeoffs for Monotone Circuits

Mika Göös·Gilbert Maystre·Kilian Risse·Dmitry Sokolov

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Abstract

We exhibit a monotone function computable by a monotone circuit of quasipolynomial size such that any monotone circuit of polynomial depth requires exponential size. This is the first size-depth tradeoff result for monotone circuits in the so-called supercritical regime. Our proof is based on an analogous result in proof complexity: We introduce a new family of unsatisfiable 3-CNF formulas (called bracket formulas) that admit resolution refutations of quasipolynomial size while any refutation of polynomial depth requires exponential size.

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Mika Göös, Gilbert Maystre, Kilian Risse, Dmitry Sokolov. 2024-11-21. Supercritical Tradeoffs for Monotone Circuits. https://arxiv.org/abs/2411.14268

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