The Modeling and Complexity of Dynamical Systems by Means of Computation and Information Theories

We present the modeling of dynamical systems and finding of their complexity indicators by the use of concepts from computation and information theories, within the framework of J. P. Crutchfield's theory of ε-machines. A short formal outline of the ε-machines is given. In this approach, dynamical systems are analyzed directly from the time series that is received from a properly adjusted measuring instrument. The binary strings are parsed through the parse tree, within which morphologically and probabilistically unique subtrees or morphs are recognized as system states. The outline and precise interrelation of the information-theoretic entropies and complexities emanating from the model is given. The paper serves also as a theoretical foundation for the future presentation of the DSA program that implements the ε-machines modeling up to the stochastic finite automata level.