Optimal Unambiguous DNFs and the Alon-Saks-Seymour Conjecture Revisited
Score
76给出多项最优下界，多个此前仅知近似结果的开放问题被完全解决。
构造与证明完整，技术深度高，结果清晰且相互关联。
虽属理论结果，但对查询复杂度与学习理论提供了直接可用的下界工具。
发表于 arXiv 最新版本，延续并改进了近期关键工作，处于研究前沿。
arXiv 预印本，但作者为领域内知名团队，且参与过相关顶会工作。
Base 84.5 × T2 Source weight ×0.9 = 76
Curation line 70Selected
Why selected
The paper delivers multiple optimal results with significant technical contributions and far-reaching implications across several subfields, with high information density.
AI commentary
「The most striking aspect of this paper is how it unifies several seemingly independent optimal lower bounds under a single combinatorial construction, with solid proof techniques. If you work in communication complexity, Boolean function complexity, or learning theory, these results are almost directly citable; even if you just appreciate elegant connections between complexity models, this paper is worth reading.」
Quick overview
This paper constructs unambiguous DNFs of width O(n) with 0-certificate complexity Ω(n²), and uses their special structure to prove a lifting theorem with a constant-sized gadget that losslessly translates the certificate complexity separation into a communication complexity separation. This yields an optimal refutation of the Alon-Saks-Seymour conjecture and an optimal communication lower bound for the Clique versus Independent Set problem, improving upon previous results by Balodis, Ben-David, Göös, Jain and Kothari by several doubly logarithmic factors. Further applications include an optimal quartic separation between certificate complexity and approximate degree in query complexity, and a sample compression lower bound of Ω(√log c) for multiclass concept classes over c labels.
- Constructs unambiguous DNFs of width O(n) with 0-certificate complexity Ω(n²), achieving an optimal separation.
- Proves a lifting theorem with a constant-sized gadget that losslessly translates certificate complexity separation into communication complexity separation.
- Optimally refutes the Alon-Saks-Seymour conjecture and provides an optimal communication lower bound for Clique versus Independent Set.
- Additional applications: quartic separation between certificate complexity and approximate degree, and a sample compression lower bound of Ω(√log c) for multiclass concept classes.
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