有限对偶齐次结构上局部一致性的新充分代数条件
New Sufficient Algebraic Conditions for Local Consistency over Homogeneous Structures of Finite Duality
AI总结：
本文首次证明在有限对偶齐次结构上，某些高度1 Maltsev条件蕴含有界宽度，从而为Bodirsky-Pinsker猜想中一大类无限域CSP模板建立了可解性结果。
摘要：
Bulatov 和 Zhuk 对 Feder-Vardi 二分性猜想的解决路径表明，越来越一般的代数条件能够为满足这些条件的有限域约束满足问题（CSPs）模板推出多项式时间算法。这些研究促成了适当的高度 1 Maltsev 条件的发现，这些条件刻画了有界严格宽度、有界宽度、few-subpowers 算法的适用性以及许多其他性质。对于处于类似的无限域 CSP 的 Bodirsky-Pinsker 猜想范围内的问题，此前只能对有界严格宽度这一概念找到这样的刻画，其证明本质上与有限情形相同。在本文中，我们提供了第一个非平凡的结果，证明某些高度 1 Maltsev 条件蕴含了有界宽度，并因此蕴含可解性，适用于 Bodirsky-Pinsker 猜想中一个自然的模板子类，该子类包括文献中的许多模板以及尚无复杂性分类的模板。
英文摘要：
The path to the solution of Feder-Vardi dichotomy conjecture by Bulatov and Zhuk led through showing that more and more general algebraic conditions imply polynomial-time algorithms for the finite-domain Constraint Satisfaction Problems (CSPs) whose templates satisfy them. These investigations resulted in the discovery of the appropriate height 1 Maltsev conditions characterizing bounded strict width, bounded width, the applicability of the few-subpowers algorithm, and many others. For problems in the range of the similar Bodirsky-Pinsker conjecture on infinite-domain CSPs, one can only find such a characterization for the notion of bounded strict width, with a proof essentially the same as in the finite case. In this paper, we provide the first non-trivial results showing that certain height 1 Maltsev conditions imply bounded width, and in consequence tractability, for a natural subclass of templates within the Bodirsky-Pinsker conjecture which includes many templates in the literature as well as templates for which no complexity classification is known.
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