OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Proves Khot's 2-to-1 Games Conjecture with perfect completeness: for every fixed rational δ∈(0,1), it is NP-hard to distinguish satisfiable games from games whose optimum is at most δ, on explicit unweighted instances. The alphabet depends only on δ, and every right-hand label has exactly two preimages under each constraint map.
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We prove the 2-to-1 Games Conjecture with perfect completeness. For every fixed rational δ∈(0,1), it is NP-hard to distinguish satisfiable 2-to-1 games from games of value at most δ, with a fixed alphabet and an explicitly listed unweighted multiset of constraints.
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