无限域CSP的有界宽度层级坍缩：当对称性足够时
Collapsing the bounded width hierarchy for infinite-domain CSPs: when symmetries are enough
AI总结：
本文证明具有规范伪WNU多态性的关系结构具有低宽度，导致无限域CSP有界宽度层级坍缩，并给出相关刻画，扩展了有限结构结果。
摘要：
我们证明了具有特定多态性（即所有元数 $n \geq 3$ 的规范伪WNU运算）的关系结构具有低关系宽度。这意味着文献中研究的众多无限域CSP类别的有界宽度层级发生坍缩。此外，我们获得了一元结构的一阶还原的有界宽度刻画，以及等价于Datalog程序的MMSNP句子的刻画，回答了Bienvenu、ten Cate、Lutz和Wolter提出的问题。特别是，在这些情况下，有界宽度层级也发生坍缩。我们的结果扩展了Barto和Kozik刻画有限结构有界宽度的定理的范围，并展示了无限域CSP在其他领域的适用性。
英文摘要：
We prove that relational structures admitting specific polymorphisms (namely, canonical pseudo-WNU operations of all arities $n \geq 3$) have low relational width. This implies a collapse of the bounded width hierarchy for numerous classes of infinite-domain CSPs studied in the literature. Moreover, we obtain a characterization of bounded width for first-order reducts of unary structures and a characterization of MMSNP sentences that are equivalent to a Datalog program, answering a question posed by Bienvenu, ten Cate, Lutz, and Wolter. In particular, the bounded width hierarchy collapses in those cases as well. Our results extend the scope of theorems of Barto and Kozik characterizing bounded width for finite structures, and show the applicability of infinite-domain CSPs to other fields.
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