A new approach to the study of dynamical systems, based on J. P. Crutchfields’s theory of є-machines, is presented. The goal is to find a model by inferring solely from a time series. A formal connection between symbolic dynamic and the parsing of the time series is made, and stochastic finite automata (SFA) are derived from the class of finite automata (FA). The general algorithm for construction of є-machines is explained, with emphasize on its specialization to reconstruction of SFA. A notion of statistical complexity is introduced as a qualitatively new measure for structural complexity or realistic systems. Guided by the principles of object-oriented programming, a software platform for the reconstruction of SFA is implemented. A parse tree, defined as a special kind of binary tree, arises as the first level of reconstruction process. Original algorithms implementing preorder, postorder and inorder traverse through the tree structure are devised. An algorithm for comparison of (sub)trees checks their morphological and probabilistic structure, and makes a key role in the process of finding of unique morphs. The latter presents the states of SFA, and the conditional transitional probabilities provide their stochastic properties. The program was tested and presented on a number of example systems. Resulting SFA-based models and corresponding statistical parameters are given. A preliminary investigation of nonlinear system governed by Logistic map is made for several values of its parameter, especially for Misiurewicz and the critical parameter at the first period-doubling onset of chaos. The results obtained are consistent with those of the author of the theory. The clarity of the binary tree interface helps to control the results of the modeling. Additional in-formation obtained from the morph-finding algorithm enables the minimization of the model, i.e. the optimization of its size regarding the probability difference parameter.