Tractability and Learnability Arising from Algebras with Few Subpowers

A constraint language $\Gamma$ on a finite set A has been called polynomially expressive if the number of n-ary relations expressible by $\exists\wedge$-atomic formulas over $\Gamma$ is bounded by $\exp(O(n^k))$ for some constant k. It has recently been discovered that this property is characterized by the existence of a $(k+1)$-ary polymorphism satisfying certain identities; such polymorphisms are called k-edge operations and include Mal'cev …