Supercritical Tradeoffs for Monotone Circuits
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909398385819648 |
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| author | Göös, Mika Maystre, Gilbert Risse, Kilian Sokolov, Dmitry |
| author_facet | Göös, Mika Maystre, Gilbert Risse, Kilian Sokolov, Dmitry |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14268 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Supercritical Tradeoffs for Monotone Circuits Göös, Mika Maystre, Gilbert Risse, Kilian Sokolov, Dmitry Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 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. |
| title | Supercritical Tradeoffs for Monotone Circuits |
| topic | Computational Complexity F.2.2; F.1.3; I.2.3; F.4.1 |
| url | https://arxiv.org/abs/2411.14268 |