We prove that a nonaffine latin quandle (also known as left distributive quasigroup) of order [Formula: see text] exists if and only if [Formula: see text] or [Formula: see text]. The construction is expressed in terms of central extensions of affine quandles.
We consider constraint satisfaction problems whose relations are defined in first-order logic over any uniform hypergraph satisfying certain weak abstract structural conditions. Our main result is a P/NP-complete complexity dichotomy for such CSPs. Surprisingly, the large class of structures under consideration falls into a mixed regime where neither the classical complexity reduction to finite-domain CSPs can be used as a black box, nor does the class exhibit order properties, known to prevent the application of this reduction. We introduce an algorithmic technique inspired by classical notions from the theory of finite-domain CSPs, and prove its correctness based on symmetries that depend on a linear order that is external to the structures under consideration.
We prove that a non-affine latin quandle (also known as left distributive quasigroup) of order 2 k exists if and only if k = 6 or k ≥ 8. The construction is expressed in terms of central extensions of affine quandles.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.