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New DNF construction refutes Alon-Saks-Seymour conjecture

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Researchers have developed a new construction for unambiguous Disjunctive Normal Forms (DNFs) that exhibit a significant separation between their width and certificate complexity. This construction leads to an optimal refutation of the Alon-Saks-Seymour conjecture and provides an improved communication lower bound for the Clique versus Independent Set problem. The work also yields optimal separations in query complexity and learning theory, including a quartic separation between certificate complexity and approximate degree, and a lower bound for multiclass concept classes. AI

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New DNF construction refutes Alon-Saks-Seymour conjecture

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COVERAGE [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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