Structure in Communication Complexity and Constant-Cost Complexity Classes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913210171392000 |
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| author | Hatami, Hamed Hatami, Pooya |
| author_facet | Hatami, Hamed Hatami, Pooya |
| contents | Several theorems and conjectures in communication complexity state or speculate that the complexity of a matrix in a given communication model is controlled by a related analytic or algebraic matrix parameter, e.g., rank, sign-rank, discrepancy, etc. The forward direction is typically easy as the structural implications of small complexity often imply a bound on some matrix parameter. The challenge lies in establishing the reverse direction, which requires understanding the structure of Boolean matrices for which a given matrix parameter is small or large. We will discuss several research directions that align with this overarching theme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14623 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Structure in Communication Complexity and Constant-Cost Complexity Classes Hatami, Hamed Hatami, Pooya Computational Complexity Several theorems and conjectures in communication complexity state or speculate that the complexity of a matrix in a given communication model is controlled by a related analytic or algebraic matrix parameter, e.g., rank, sign-rank, discrepancy, etc. The forward direction is typically easy as the structural implications of small complexity often imply a bound on some matrix parameter. The challenge lies in establishing the reverse direction, which requires understanding the structure of Boolean matrices for which a given matrix parameter is small or large. We will discuss several research directions that align with this overarching theme. |
| title | Structure in Communication Complexity and Constant-Cost Complexity Classes |
| topic | Computational Complexity |
| url | https://arxiv.org/abs/2401.14623 |