There exist two conjectures for constraint satisfaction problems (CSPs) of reducts of finitely bounded homogeneous structures: the first one states that tractability of the CSP of such a structure is, when the structure is a model-complete core, equivalent to its polymorphism clone satisfying a certain nontrivial linear identity modulo outer embeddings. The second conjecture, challenging the approach via model-complete cores by reflections, states that tractability is equivalent to the linear identities (without outer embeddings) satisfied by its polymorphisms clone, together with the natural uniformity on it, being nontrivial. We prove that the identities satisfied in the polymorphism clone of a structure allow for conclusions about the orbit growth of its automorphism group, and apply this to show that the two conjectures are equivalent. We contrast this with a counterexample showing that [Formula: see text]-categoricity alone is insufficient to imply the equivalence of the two conditions above in a model-complete core. Taking another approach, we then show how the Ramsey property of a homogeneous structure can be utilized for obtaining a similar equivalence under different conditions. We then prove that any polymorphism of sufficiently large arity which is totally symmetric modulo outer embeddings of a finitely bounded structure can be turned into a nontrivial system of linear identities, and obtain nontrivial linear identities for all tractable cases of reducts of the rational order, the random graph, and the random poset. Finally, we provide a new and short proof, in the language of monoids, of the theorem stating that every [Formula: see text]-categorical structure is homomorphically equivalent to a model-complete core.

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寡态克隆中的方程和ω-分类结构的约束满足问题

有限有界同质结构约简的约束满足问题（CSPs）存在两种猜想：第一种猜想是这种结构的 CSP 的易处理性是，当结构是模型完备的核时，它的多态克隆等价于满足某个非平凡的线性恒等模外嵌入。第二个猜想通过反射通过模型完整核心挑战该方法，指出易处理性等同于其多态性克隆所满足的线性恒等式（没有外部嵌入），以及其上的自然均匀性，是不平凡的。我们证明了结构的多态性克隆中满足的恒等式可以得出关于其自同构群的轨道增长的结论，并以此证明这两个猜想是等价的。我们将其与一个反例进行对比，该反例表明 [公式：参见文本]-单独的分类性不足以暗示上述两​​个条件在模型完整核心中的等价性。采用另一种方法，我们随后展示了如何利用均质结构的 Ramsey 特性在不同条件下获得类似的等价性。然后，我们证明任何足够大的多态性，即有限有界结构的完全对称模外嵌入，都可以转化为线性恒等式的非平凡系统，并为所有可处理的有理阶约简的情况获得非平凡线性恒等式，随机图和随机偏序集。最后，我们用幺半群语言提供了一个新的简短证明，该定理说明每个 [公式：