We consider constraint satisfaction problems whose relations are defined in first-order logic over any uniform hypergraph satisfying certain weak abstract structural conditions. Our main result is a P/NP-complete complexity dichotomy for such CSPs. Surprisingly, the large class of structures under consideration falls into a mixed regime where neither the classical complexity reduction to finite-domain CSPs can be used as a black box, nor does the class exhibit order properties, known to prevent the application of this reduction. We introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration.

翻译：我们考虑一类约束满足问题，其关系在一阶逻辑中定义于任意满足特定弱抽象结构条件的均匀超图之上。我们的主要结果是此类CSP的P/NP完全复杂度二分性。令人惊讶的是，所考虑的这一大类结构处于混合状态：既不能将经典复杂度归约到有限域CSP作为黑箱使用，也不具备已知可阻止该归约应用的序性质。我们引入一种受有限域CSP理论中经典概念启发的算法技术，并基于依赖外在线性序（该序独立于所考虑的结构）的对称性证明其正确性。