Resumen
In this paper we consider the representation of iterations of finite languages using special nondeterministic finite automata. For two iterated languages, a special equivalence relation is defined. We give the reduction of the conditions for the fulfillment of this relation to the definition of the equivalence of two nondeterministic finite automata, based on two given finite languages. Also we are considering a trivial proof of the regularity of the morphic preimage of regular language; this proof is related to the issues. In addition, using the equivalence relation under consideration hypotheses are formulated on the existence of a polynomial-time algorithm for the construction of an inverse morphism, possessing the specified special properties, as well as the relationship of the problems we are considering with the question of the possible equality of classes P=NP