In this multidisciplinary work we describe, implement, and apply the modeling of one-dimensional dynamical systems in which the computational model with added stochastic properties is built solely from the received binary time series. The introductory theoreti-cal chapters show the correctness of such an approach. Symbolic dynamics is connected to the encoding in the measuring-modeling channel and approximated by the finite-length substrings. Among a few presented methodologies, the Crutchfield theory of ε-machines is selected as the best for the modeling from a time series. The basic ε-machine is presented by a stochastic finite automaton (SFA), which is here derived from the class of finite automata (FA). The equality of the stochastic nondeterministic finite automata (SNFFA) to the edge-output hidden Markov models (EOHMM) is illustrated. The more complex automata suitable for the higher-level ε-machines are also presented. The basic concepts of the theory of ε-machines are given their operational versions: (L, δ)-equivalent causal states and their practical substitutions ─ (L, δ)-morphs (further, morphs), which define the classes of equivalence. Known states and their transitions' probabilities define the transition tensor, and thus an ε-machine and its SFA. The num-ber of the morph-correlated symbols and the morph-investigated correlation length are introduced, as well as the correlation length of the SFA-model and the length of its re-current cycle. The reconstruction of ε-machines is a hierarchical process. From the time series, the parse tree of height D is created, wherefrom morphs are found as (L, δ)-unique subtrees. These ε-(sub)trees ─ with leaves at the constant level (L) D ─ are theo-retically described. Their statistics is based on the average number bl of children from an l-level node. The main computational contributions of this work are original FM and TFM algo-rithms. They find morphs (states), their mutual transitions and probabilities, and thus define the SFA-model of a system. For given L and δ, FM algorithm finds the deepest morph on level lDM and generally stops before having checked all the subtrees. This is called (potential) superficiality. The condition for a regular SFA is lDM + L + 1 ≤ D. The concept of comprehensive modeling is introduced. By the variation of L and δ ─ with a chosen resolution for the latter ─ the whole space of the FM algorithm solutions for a parse tree of height D is being explored. The thorough, TFM algorithm first investigates all the subtrees in the parse tree and then removes those which are (L, δ)-equivalent to earlier subtrees. It confirms the correctness of the FM algorithm results. Both algorithms guarantee the minimality and determinism of their regular SFA-models, which is their main advantage over other algorithms of the same purpose. A complete information-theoretical analysis of the time series and the SFA-model is given. The corresponding entropy rates and various complexities are defined. An original expansion of the SFA total entropy to the sum of statistical complexity and the model entropy rate is present-ed. It is proved that the latter can be resolved as the sum of the entropy rate of the time series emitted from the model and the transition indeterminacy, or the sum of the entro-py rate of the Markov source and the newly introduced symbol-per-transition entropy rate. All defined quantities are calculated for various dynamical systems and proven for the periodic ones. The modeling up to the SFA level is realized by our original DSA programming tool. The implementation of data structures and algorithms used in its three main program-ming modules is presented. Inspection of the time series, main (parse) tree, morphs and the created models is possible via graphical user interfaces. The time-space complexity of the tree-feed process for a statistically relevant main tree is generally exponential in the tree height D. Correctness of the original nonrecursive tree-traversal algorithms was proven, and they were compared to the recursive versions. FM algorithm is upgraded from its first version. Its implementation is described in detail, and the implementation of the extensive TFM algorithm in its essential parts. The exhaustive analysis of FM al-gorithm time complexity is made for the cases of different parse trees and different ways of its operation. For general systems, this complexity is exponential in different linear combinations of parameters L and D and in the worst case in their difference 2D − L. DSA program was applied for the modeling of numerous systems. For their parse ε-trees, the utmost levels of statistical consistency had been determined, so that their morphs were being found from the consistent main trees. Those levels were theoretically connected to the accuracy of numerical calculation and Lyapunov exponent of the sys-tem. For periodical, rule-defined, and fully quasi-stochastic systems, both, FM and TFM algorithms give the exact SFA-models. The same is true for the logistic map at the onset of chaos by the end of the period-doubling route, for which the number of SFA states diverge with increasing morph height L. Here, more plausible SFA-models were obtained than previously known. Also, on a higher level, a finite register machine is confirmed. Logistic maps at the intermittency chaos, Misiurewicz parameter, and near the climax of chaos show structure mixed with quasi-stochasticity. The comprehensive modeling of these systems for a given range of L and decreasing δ gives more and more precise SFA-models, with increasing number of states. Based on their graphs and the calculated in-formation-theoretic indicators, the best representative models are chosen among them. Some of them were confirmed by the TFM algorithm. Such a complex modeling task can be effectively accomplished by a human modeler with the aid of the DSA program. By this, we have provided a functional modeling platform that is suitable for further upgrades and generalizations.