Block composition algorithm for constructing orthogonal n-ary operations

Abstract

We propose an algorithm for constructing orthogonal n-ary operations which is called a block composition algorithm here. Input data of the algorithm are two series of differ ent arity operations being distributed by blocks. The algorithm consists of two parts: composition algorithm for constructing n-ary operations with orthogonal retracts from given blocks of operations and block-wise recursive algorithm for constructing orthogonal n-ary operations from obtained operations. Obtained results are illustrated by examples of orthogonal n-ary operations which are constructible by block-wise recursive algorithm and non-constructible by the well-known trivial recursive algorithm.