In Theorem 36 we saw that it is $\mathsf{NP}$-hard to $(1-\delta_0, 1)$-approximate Max-E$3$Sat for some positive but inexplicit constant $\delta_0$. You might wonder how large $\delta_0$ can be. The natural limit here is $\frac18$ because there is a very simple algorithm which satisfies a $\frac78$-fraction of the constraints in any Max-E$3$Sat instance:

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## Recent comments

Yongzhi: I think that the domain of the function g in Fact 21 should ...El Manolo: I can't figure out ex.12 b) and c) in the proposed way. Tha...R.: Is $\rho\neq 0$ required in 1(f)?R.: Typo: they introduced also introduced “tribes”Chin Ho Lee: they introduced also introduced “tribes” -> they also int...Mathias Niepert: This is not a correction but a question concerning the stabi...Ravi Boppana: In the hint to Exercise 21, should $(-\frac{1}{2} + \frac{\s...