Complexity Estimation of Automata Models with Use the Discrete RIV-functions

The depiction of laws of system functioning is used in methods for deciding control problems, synthesis, and analysis of discrete determined dynamic systems (automatons). The phase trajectories, which define system behaviour, are systematised and shown in phase images. The wide range of phase pictures created by V. A. Tverdokhlebov is due to their uniform form – symbolical and numerical graphs in which points correspond to geometrical curves. The related automaton mapping will be translated to a numerical graph with points situated on geometrical curves when the automaton is represented by a geometrical image. V. A. Tverdokhlebov’s method of extracting laws of functioning of the automaton of sequence of the second coordinates of points, accurate within number of input signals, from a geometrical image allows research of laws of functioning of automatons to be reduced to research of properties of numerical sequences. On the basis of geometrical representations of laws and the usage of discrete riv-functions, this study proposes the evaluation of complexity of rules of functioning of discrete determined dynamic systems (automatons). Is responsible for analysing about 10 million discrete riv-functions. The least and greatest number of states at the minimal automaton from the set of automatons described by riv-function are used as complexity indicators.

Author (S) Details

Anton Epifanov
Institute of Problems of Precision Mechanics and Control Sciences of Russian Academy of Sciences, Saratov, Russia.

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