Are most Boolean functions determined by low frequencies?
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912164376215552 |
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| author | Vershynin, Roman |
| author_facet | Vershynin, Roman |
| contents | We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function $f: \{-1,1\}^p \to \{-1,1\}$ there exists a function $f': \{-1,1\}^p \to (-1,1)$ that has the same frequencies as $f$ up to dimension $(1/2-o(1))p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_13143 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Are most Boolean functions determined by low frequencies? Vershynin, Roman Combinatorics 06E30, 42C10, 60D05, 52C35 We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function $f: \{-1,1\}^p \to \{-1,1\}$ there exists a function $f': \{-1,1\}^p \to (-1,1)$ that has the same frequencies as $f$ up to dimension $(1/2-o(1))p$. |
| title | Are most Boolean functions determined by low frequencies? |
| topic | Combinatorics 06E30, 42C10, 60D05, 52C35 |
| url | https://arxiv.org/abs/2401.13143 |