We develop the novel machinery of smooth approximations, and apply it to confirm the CSP dichotomy conjecture for first-order reducts of the random tournament, various homogeneous graphs including the random graph, and for expansions of the order of the rationals. Apart from obtaining these dichotomy results, we show how our new proof technique allows to unify and significantly simplify the previous results from the literature. For all but the last structure, we moreover characterize those CSPs which are solvable by local consistency methods, again using the same machinery.

中文翻译：

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有限界齐次结构上的平滑近似和 CSP

我们开发了新的平滑逼近机制，并将其应用于验证随机锦标赛的一阶约简、包括随机图在内的各种齐次图以及有理数阶展开的 CSP 二分猜想。除了获得这些二分法结果之外，我们还展示了我们的新证明技术如何统一并显着简化先前文献中的结果。对于除了最后一个结构之外的所有结构，我们还表征了那些可通过局部一致性方法解决的 CSP，再次使用相同的机制。