New DNF construction refutes Alon-Saks-Seymour conjecture

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

• paper
• other

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