THE CHARACTERIZATION OF BINARY RELATION HOMOMORPHISMS

Abstract A characterization theorem is derived for homomorphisms of one binary relation to another. The characterization theorem states that any homomorphism from one relation to another can be represented as the intersection of some basis relations. Furthermore, appropriate intersections of the basis relations define a relation homomorphism. The characterization theorem leads to an efficient algorithm for determining all the homomorphisms from one relation to another: first find the basis relations, and then use the basis relations to generate all single-valued relations which then will be all the homomorphisms from one relation to the other. Specialization of the procedure easily determines whether two relations or digraphs are isomorphic.