We study the approximability of predicates on $k$ variables from a
domain $[q]$, and give a new sufficient condition for such predicates
to be approximation resistant under the Unique Games Conjecture.
Specifically, we show that a predicate $P$ is approximation resistant
if there exists a balanced pairwise independent distribution over
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We study constraint satisfaction problems on the domain $\{-1,1\}$, where the given constraints are homogeneous linear threshold predicates. That is, predicates of the form $\mathrm{sgn}(w_1 x_1 + \cdots + w_n x_n)$ for some positive integer weights $w_1, \dots, w_n$. Despite their simplicity, current techniques fall short of providing a classification ... more >>>