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]
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- Alon-Saks-Seymour conjecture
- Ben-David
- Clique versus Independent Set problem
- Columba
- FOCS 2021
- Göös
- Jain
- Kothari
- SICOMP 2023
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