CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917572584144896 |
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| author | Bodnar, Levente |
| author_facet | Bodnar, Levente |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits Bodnar, Levente Computational Complexity 68Q06 F.1.3; F.2.3 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. |
| title | CLIQUE as an AND of Polynomial-Sized Monotone Constant-Depth Circuits |
| topic | Computational Complexity 68Q06 F.1.3; F.2.3 |
| url | https://arxiv.org/abs/2401.12094 |