Finite state machines and automata languages are effective instruments of describing and modeling software systems. For research of the automata language properties one can use approaches, that traditionally belong to the field of data analysis. For example, the problem of automata language recognition can be viewed as the problem of classifying all words over a given alphabet. One class of words is defined by an automata language. Another class of words is the complement of this automata language. In the classical formulation of this task it is assumed that the classifier is completely defined. It is assumed that the finite state machine that recognizes the automata language or its complement language, is defined. In this case the solution is to minimize the classifier to reduce its computational complexity. In this article, it is assumed that the classifier is unknown. It specifies only the training sample, which contains a finite number of reference representatives of the automata language and complement of this automata language. Accordingly, the task is to build an approximate classifier by analyzing the structure of the training sample elements. To do this, a new concept of approximate automata that acts as an approximation of the classifier is introduced. As the quality characteristics of the solution of the problem we introduce the concepts of weak and strong correctness of the approximate classifier. We investigate the relationship of these characteristics. An algorithm for constructing approximate machine automata that has the property of strong correctness and solve task of words classification is described.