Smooth Approximations and Relational Width Collapses
Antoine Mottet, Tomáš Nagy, Michael Pinsker, Michał Wrona · Homo Politicus (Academy of Humanities and Economics in Lodz) · 2021
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 et al.. In particular, the bounded width hierarchy collapses in those cases as well.