We study the complexity of infinite-domain constraint satisfaction problems: our basic setting is that a complexity classification for the CSPs of first-order expansions of a structure $\mathfrak A$ can be transferred to a classification of the CSPs of first-order expansions of another structure $\mathfrak B$. We exploit a product of structures (the algebraic product) that corresponds to the product of the respective polymorphism clones and present a complete complexity classification of the CSPs for first-order expansions of the $n$-fold algebraic power of $(\mathbb{Q};<)$. This is proved by various algebraic and logical methods in combination with knowledge of the polymorphisms of the tractable first-order expansions of $(\mathbb{Q};<)$ and explicit descriptions of the expressible relations in terms of syntactically restricted first-order formulas. By combining our classification result with general classification transfer techniques, we obtain surprisingly strong new classification results for highly relevant formalisms such as Allen's Interval Algebra, the $n$-dimensional Block Algebra, and the Cardinal Direction Calculus, even if higher-arity relations are allowed. Our results confirm the infinite-domain tractability conjecture for classes of structures that have been difficult to analyse with older methods. For the special case of structures with binary signatures, the results can be substantially strengthened and tightly connected to Ord-Horn formulas; this solves several longstanding open problems from the AI literature.
翻译：我们研究了无限范围制约的满意度问题的复杂性:我们的基本背景是,对结构的一阶扩展的CSP的复杂度分类 $\ mathfrak A$ 能够转移到另一结构的一阶扩展的CSP的分类 $\ mathfrak B$。我们开发了一个结构的产物(代数产品),这种产物与各个多形态克隆的产物相对应,并且对CSP的一阶扩展的CSP的复杂性分类,用于美元(mathbb*; < $)的美元(mathbb*; < $) 的一阶扩展的美元结构的一阶扩展的复杂度分类。各种代数种计算法和逻辑方法都证明了这一点,同时了解了另一个结构的多层次扩展的多层次扩展 $(\ mathblogb=) ; $- recaldologal-albal-albalbalbalislational-allial-ral-ral-rational-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-ral-lational-lation-ral-lation-lation-lation-lation-lational-lation-lislislism-lupal-lation-lislisl) 和可以使我们卡-lation-lus-li-li可以使卡-lation-lation-lation-lation-al-al-al-al-al-al-al-al-l-l-l-l-l-l-l-l-l-l-l-l-al-al-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-l-
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