2020 year, volume 24, issue 2 (PDF)

Bektashev R.A. Using AI approach to plan personal learning strategy

In this article the problem of planning personal learning strategy is set and results of applying various approaches to its solution are presented.

Keywords: computer education system, sequence elements prediction, neural network, recurrent neural network, compact prediction tree.

Biryukova V.A. The technology of knowledge distillation for training neural networks on example of binary classification

Using the technology of training neural networks, the knowledge distillation, models were obtained that solve the binary classification problem with the productivity that is about five times higher than the performance of the teacher network with an insignificant drop in quality. The convolutional neural network ResNet-18 was trained in two ways by this technology (using the pre-trained network ResNet-50) and by the classical method. The concept of the degree of uncertainty of the model on objects’ set is introduced as the quantity of the deviation of the neural network predictions from the values accepted for the answer. The experiments on the recursive application of the knowledge distillation technology were also conducted.

Keywords: knowledge distillation, binary classification, residual neural network, convolutional neural network, degree of uncertainty of the model on objects’ set, recursive training of neural networks.

Alekseev D.V. Necessary and sufficient conditions for the existence of an image with a given code

The article introduces an image encoding function which is invariant with respect to affine transform. The properties of the encoding funciton are investigated. Necessary and sufficient conditions are found for a given set of numbers to be a code of nonsingulari image.

Keywords: image code, image encoding, affine equivalence.

Muravev A.K. On the self-organizing system of the traffic lights that ensure uninterrupted traffic

The present paper considers the cooperative game about the transport delivery on the rectangular grid. The concepts of congestion and cars collision on it, as well as the automata as the agents in the traffic lights of the grid regulating movement of transport, are introduced. It’s proved that there exists a structure of the automata with local area of visibility leading to the self-organization of the system of traffic lights ensuring an arbitrarily long, correct transport delivery without any congestions and cars collisions for any number of grid’s outputs.

Keywords: cooperative game, delivery, traffic organization, agent, homogeneous structure, automaton.

Pankratieva V.V. Minimization of the Number of States of a Fuzzy Automaton Using Interval Pattern Concepts

Relationship between the problem of minimization of the number of states of fuzzy automata and the problem of mining of interval pattern concepts with maximum extent is considered. The clustering method based on interval pattern concept mining combines states of a fuzzy automaton into subsets with similar patterns of confidence of transition into other states, where patterns are considered close to each other if the distance between them is bounded by a predetermined parameter σ. It is shown that for a certain type of fuzzy transition matrices the behavior of the original fuzzy automaton, as well as the behavior of the minimized one, eventually stabilizes. Moreover, it is proved that the membership value of each word recognized by the fuzzy automaton does not decrease after minimization. This fact allows comparing the fuzzy language recognized by the original automaton and the language recognized by the minimized automaton.

Keywords: fuzzy automata, interval pattern concepts, fuzzy languages.

Gasanov E.E. Celluar automata with locators

This article introduce new type of math object — cellular automaton with locators. It was created by implementing new functionality for automaton - broadcasting “on-air” signals and retrieving generalized “on-air” signal from all elementary automata. This article highlights some tasks whose solution will be greatly simplified by using cellular automaton with locators instead of traditional cellular automata.

Keywords: cellular automata, homogeneous structures, firing squad problem, motion picture design, constructing the shortest path.

Manshilin O.G. Prediction of superword segments

The automaton predicts the character of the input sequence, if it outputs this character at the previous time. The paper introduces the concept of the degree of prediction on a superword segments. The question of the relationship between prediction on superword segments and prediction on superwords is investigated. We obtained results that allow us to judge the degree of prediction on superword segments if we know degree of prediction on superword and vice versa.

Keywords: predicting automaton, prediction of superwords with automatons, prediction degree on finite subsequency.

Muravev N.V. Decidability of the order problem for linear automata

We consider the order problem for linear automata. A finite order criterion for linear automata is presented that provides an algorithm solving this problem. An upper bound of linear automata orders is proved.

Keywords: finite automata, linear automata, order in semigroup.

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