Smooth Approximations and Relational Width Collapses

02/15/2021

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by   Antoine Mottet, et al.

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We prove that relational structures admitting specific polymorphisms (namely, canonical pseudo-WNU operations of all arities n ≥ 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.