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.
翻译:我们证明,允许特定多形态结构(即所有等域的卡通假WNU操作$\geq 3美元)的关系结构宽度较低,这意味着文献中研究的无数类无边域CSP的宽度结构崩溃了。 此外,我们获得了对单体结构一阶脱钩的封闭宽度的定性,对MMSNP判决的定性相当于数据仪程序,回答了Bienvenu、10 Cate、Lutz和Wolter提出的问题。特别是,在这些案例中,约束的宽度等级也崩溃了。