arXiv Machine Learning By Chirag Pabbaraju

Optimal Unambiguous DNFs and Alon-Saks-Seymour

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arXiv:2608. 02533v1 Announce Type: cross Abstract: We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $\Omega(n^2)$.

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Optimal Unambiguous DNFs and Alon-Saks-Seymour

We construct unambiguous DNFs having width $O(n)$ but $0$-certificate complexity $Ω(n^2)$. By utilizing the special structure of these DNFs, we prove a lifting theorem with a constant-sized gadget that lifts the DNF to a communication problem, while losslessly translating the separation in certificate complexity to a separation in communication complexity.

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