Theoretical computer science · Oct 6, 2026

Perfect completeness for 2-to-1 games

Proves Khot's 2-to-1 Games Conjecture with perfect completeness: for every fixed rational δ∈(0,1)\delta\in(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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