Regular Sets of Operations
Hajime Machida, Jovanka Pantovic and Ivo G. Rosenberg
Regular operations on a (2k-1)-element set are operations having a particular property that induces 1-1 correspondence with the set of all hyperoperations on a k-element set. It implies that the lattice of hyperclones on a k-element set is isomorphic to the lattice of regular sets on a (2k-1)-element set. We introduce this concept formally and present a Galois connection Inv-rPol for which F = rPol Inv F for each regular set F. Finally, we present all maximal regular sets on a three-element set, determined by Tarasov.
Keywords: Hyperclone, multiclone, regular set