CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits

Levente Bodnar

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arXiv · 2401.12094

CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits

Levente Bodnar

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Abstract

This paper shows that calculating $k$-CLIQUE on $n$ vertex graphs, requires the AND of at least $2^{n/4k}$ monotone, constant-depth, and polynomial-sized circuits, for sufficiently large values of $k$. The proof relies on a new, monotone, one-sided switching lemma, designed for cliques.

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Levente Bodnar. 2024-01-22. CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits. https://arxiv.org/abs/2401.12094

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