Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation

05/09/2023

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by   Ali Çivril, et al.

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We provide a new approach for establishing hardness of approximation results, based on the theory recently introduced by the author. It allows one to directly show that approximating a problem beyond a certain threshold requires super-polynomial time. To exhibit the framework, we revisit two famous problems in this paper. The particular results we prove are: MAX-3-SAT(1,7/8+ϵ) requires exponential time for any constant ϵ satisfying 1/8≥ϵ > 0. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2(1-ϵ, 1/2+ϵ) requires exponential time for any constant ϵ satisfying 1/4≥ϵ > 0.