Clones and hyperidentities (Q1806078)

Let \({\mathbf A}\) be an algebra. An identity in \({\mathbf A}\) is called a hyperidentity in \({\mathbf A}\) if it is satisfied after replacing the operation symbols by terms of the corresponding arity. The paper gives a survey on the theory of hyperidentitites and its connection to clones. Hyperidentities in \({\mathbf A}\) correspond to identities in the clone of term operations of \({\mathbf A}\). In this way clones can be described by hyperidentities. This approach is applied to the functional completeness problem, i.e. to the question when given operations on a set already generate all operations on this set.