Tractability and learnability arising from algebras with few subpowers

A k-edge operation ϕ on a finite set A is a k + 1-ary operation that satisfies the identities ϕ(x, x, y, . . . , y) ≈ ϕ(x, y, x, y, . . . , y) ≈ y and ϕ(y, y, y, x, y, . . . , y) ≈ ϕ(y, y, y, y, x, y, . . . , y) ≈ · · · · · · ≈ ϕ(y, y, y, . . . , y, x) ≈ y. We prove that any constraint language that, for some k > 1, has a k-edge operation as a polymorphism is globally tractable. Special instances of k-edge operations are Mal’cev and near-unanimity operations and so this class of tractable constraint languages includes many well known examples. mention learnability too.

• Type: Conference
• Year: 2007
• Where: LICS
• Authors: Pawel M. Idziak, Petar Markovic, Ralph McKenzie, Matthew Valeriote, Ross Willard
• Keywords: 1-ary Operation, Computer Science, K-edge Operations, LICS 2007, finite Set