2025 year, volume 29, issue 3 (PDF)

Podkolzin A.S. Introduction to Logical Processes. General diagram of the Solver’s functioning

This article describes the general layout of the mathematical problem solver. It explains how the verification process works, how to run problem solvers, and how to explore step-by-step previews. A large number of suggestions for entering and solving problems are provided.

Keywords: mathematical problem solver, logical processes, logical language, logical formalization of problems.

A. A. Khlebnikova, E. V. Bityutskaya, G. V. Kalachev, E. E. Gasanov The Use of Language Models in Automated Markup of Texts on Life Difficulties

The paper addresses the laborious nature of manual coding of qualitative data in psychological studies that use content analysis. The effectiveness of automated text markup methods utilizing modern language models such as DeepSeek, GPT-4.1, and GPT-4.1-mini is assessed, and approaches to improve markup accuracy are developed. The work is based on descriptions of dificult life situations experienced by participants in a psychological study. The study confirms the practical feasibility of using language models as a tool that significantly reduces the time spent by researchers on the initial analysis of text data.

Keywords: ontent analysis, large language model, GPT-4.1, DeepSeek, dificult life situation, coping, situation perception.

Bobrov E.A., Minenkov D.S., Yudakov D.A. Adaptive Regularized Zero-Forcing Beamforming in Massive MIMO with Multi-Antenna Users

Modern cellular networks utilize massive MIMO technology with multiple antennas. This work investigates the adaptive regularized Zero-Forsing method employing special regularization based on SVD. We conduct theoretical analysis, performance evaluation, and comparison with other methods through simulations using the Quadriga channel model.

Keywords: Telecommunications, MIMO, optimization, singular value decomposition (SVD), signal-to-interference-and-noise ratio (SINR), spectral eficiency.

Davydova D.N. Binarization of language models

Large language models are widely used in the field of natural language processing. However, despite their high eficiency, the application of large language models becomes dificult due to their high computational and memory costs. One of the ways to solve this problem is neural network quantization, that is, converting the weights and activations of the network to a representation with lower bit-width. A special case of quantization is binarization, which is the compression of network parameters to a bit-width of 1 bit. In this paper, the structure of binary neural networks is considered, an overview of current methods of language model binarization is provided, and the results obtained are described.

Keywords: natural language processing, binary neural networks, binarization, quantization, large language models.

Kozlov V.N. On three initial approximations to the formal definition of a visual image in an arbitrary visual environment

Visual image recognition is one of the central task for intelligent systems. The advancement of mathematical and theorem-based research methods in this field is significantly hampered by the lack of a complete and acceptable formal definition of the concept of a visual image in any visual environment. This paper presents an approach to such a definition using successive approximations and describes three approximations.

Keywords: visual image, image recognition, affine transformations.

Maslenikov D. O. Applying negation to strongly connected automata

The concept of the result of applying a function f, defined on its output alphabet, to an initial automaton is introduced as a minimized initial automaton implementing a certain boundedly deterministic function. A suficient condition for its strong connectivity is found. The concepts of a skeleton - a noninitial automaton without an output function - and the result of applying a function to it, as a noninitial analog of the previous definition, are also introduced. The results of applying negation to skeletons of a certain type are considered. For the result of applying negation to a strongly connected automaton with input and output alphabets {0,1}, upper and lower bounds for the number of states are obtained, for which a generalization of the concept of a cycle space to oriented graphs was considered.

Keywords: finite automaton, self-modifying finite state machine, Moore diagram, graph, cycle space.

Muravev N.V. The order problem for automata which transition and output functions lie in closed Post classes

We consider the order problem for Mealy automata with respect to the superposition operation. The splitting of the Post’s lattice of closed classes is proved based on decidability of the order problem for respective R-automata.

Keywords: Mealy automata, Post classes, algorithmic decidability.