Simple translation-invariant concepts are hard to learn - Jerrum, Mark 1955- (1991)
Abstract: "The concept class TCM of 'translation-closed monomials' was proposed by Maragos and Valiant as a natural starting point for the investigation of the computational complexity of learning translation-invariant concepts. Concepts in TCM are (satisfy assignments to) DNF formulas such as [formula], (over the variables x b0 s, x b1 s, ..., x b4 s) which are generated from a single monomial (conjunction of variables) by cyclically permuting indices, and forming the disjunction of the monomials so formed. Note that concepts in TCM are invariant under cyclic permutations of the variable set. This note investigates the computational complexity of learning TCM concepts within the Valiant (PAC) model
Keywords: Computer software; Mathematical sciences; Computational complexity