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arXiv · 2305.05676

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

Ali Çivril
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Abstract

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$(1,\frac{7}{8}+ε)$ requires exponential time for any constant $ε$ satisfying $\frac{1}{8} \geq ε> 0$. In particular, the gap exponential time hypothesis (Gap-ETH) holds. MAX-3-LIN-2$(1-ε, \frac{1}{2}+ε)$ requires exponential time for any constant $ε$ satisfying $\frac{1}{4} \geq ε> 0$.

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Ali Çivril. 2026-07-21. Scheme-Theoretic Approach to Computational Complexity. IV. A New Perspective on Hardness of Approximation. https://arxiv.org/abs/2305.05676

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