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Optimal Unambiguous DNFs Refute Alon-Saks-Seymour Conjecture

By PulseAugur Editorial · [1 sources] ·

Researchers have developed unambiguous Disjunctive Normal Forms (DNFs) with a width of O(n) but a certificate complexity of Ω(n^2). This construction, utilizing the specific structure of these DNFs, proves a lifting theorem that translates certificate complexity separation into communication complexity separation. This work provides an optimal refutation of the Alon-Saks-Seymour conjecture and an improved communication lower bound for the Clique versus Independent Set problem, surpassing previous results by several doubly logarithmic factors. AI

IMPACT Advances theoretical understanding of computational complexity, potentially impacting future algorithm design.

RANK_REASON The item describes a theoretical computer science paper with new constructions and proofs. [lever_c_demoted from research: ic=1 ai=0.4]

Read on Hugging Face Daily Papers →

AI-generated summary · Google Gemini · from 1 sources. How we write summaries →

Optimal Unambiguous DNFs Refute Alon-Saks-Seymour Conjecture

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The item describes a theoretical computer science paper with new constructions and proofs. [lever_c_demoted from research: ic=1 ai=0.4]
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COVERAGE [1]

  1. Hugging Face Daily Papers TIER_1 English(EN) ·

    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 sep…

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