Abstract
In paper are considered laws of functioning of discrete determined dynamical systems and specific processes of functioning of such systems. As basic mathematical model of laws of functioning of systems are used automata models with a fundamentally new extension of these models to models with a countable infinite sets of states. This expansion is possible thanks to the proposed and developed by Tverdohlebov V. A. the mathematical apparatus of geometrical images of automaton mappings. Are presented results of development of regularization methods for partially set automata models of systems based on use of geometrical images of automatons mappings and numerical interpolation methods. Also in paper are considered a problem of complexity estimation of laws in a whole and specific processes of functioning of dynamic systems. For these purpose are used recurrent models and methods and also a specific mathematical apparatus of discrete riv-functions. Is spent classification by complexity estimations of automata models.
Highlights
In the theory of experiments with automatons initial base is decoding of a contained of "black box"
Hibbard [3] and other authors solve following problems: criteria of existence of the decision of a problem of recognition of a contained of black box are found; the basic method of construction of experiment on automaton recognition in the set family of automatons, including construction minimum on length of simple unconditional experiment
In case, when geometrical image of automaton model of concrete discrete dynamic system is in the specified borders, can specify precisely an interval of values for number of states in the minimal form of automaton model of system without obviously constructing of the automaton and minimization
Summary
In the theory of experiments with automatons initial base is decoding of a contained of "black box". In paper are developed methods of interpolation for partially set laws of functioning of the automatons, presented by geometrical images. In the given work with use of the apparatus of geometrical images of automatons [4], it is offered and is investigated the estimation of complexity of laws of functioning of the discrete determined dynamic systems (automatons) on the basis of discrete riv-functions of kind H d,k (t) = [h1d,k (t), h2d,k (t)] , where and h1d,k (t) and h2d,k (t) - the finite discrete determined functions of a kind hd,k :{1, 2, ..., d} →{0, 1, 2, ..., k}, defined on initial segment of the natural scale, accepting values from initial segment of the natural scale and for any t, where 1 ≤ t ≤ d, d, k∈N +, h1d,k (t) ≤ h2d,k (t). T =1 In this work is offered the estimation of complexity of laws of functioning of the discrete determined dynamic systems (automatons) on the basis of geometrical representation of laws and use of discrete riv-functions. As complexity indicators are considered the minimum and maximum number of states at the minimal automaton from the set of automatons, defined by riv-function
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