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