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English(EN) Optimal Unambiguous DNFs and Alon-Saks-Seymour

新的DNF构造反驳了Alon-Saks-Seymour猜想

作者 PulseAugur 编辑部 · [1 个来源] ·

研究人员开发了一种新的无歧义析取范式（DNF）构造方法，该方法在宽度和证书复杂度之间表现出显著的分离。这种构造方法能够最优地反驳Alon-Saks-Seymour猜想，并为Clique与Independent Set问题提供了改进的通信下界。这项工作还带来了查询复杂度和学习理论中的最优分离，包括证书复杂度与近似度之间的四次分离，以及多类概念类别的下界。 AI

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新的DNF构造反驳了Alon-Saks-Seymour猜想

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报道来源 [1]

  1. arXiv cs.LG TIER_1 English(EN) · Chirag Pabbaraju ·

    Optimal Unambiguous DNFs and Alon-Saks-Seymour

    arXiv:2608.02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a comm…

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