2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174553We consider the concepts of colored terms and multi-hypersubstitutions. Studying the multi-hypersubstitutions we find out necessary and sufficient conditions a variety to be pre-complete. Finally we give an automata realization of multi-hypersubstitutions and colored terms.17 pages, 2 figures, Journal "Algebra and Discrete Mathematics", Number 3 (2007), pp. 113-131, http://adm.lnpu.edu.ua/General MathematicsRings and Algebras08B15; 03C05text