Volume 1(70)

CONTENTS

  1. Aleeva V. N., Sokolov M. P. Formation of Representations of Algorithms for Software Systems Based on the Concept of a Q-Determinant     
  2. Vlasenko A. Yu., Gorodnichev M.A., Kurbatov M.A. Debugging System of Simple Computational Models in Graph Representation     
  3. Gerb A.R., Deviatykh E. E., Omarova G. A. Optimization of the k-shortest Paths Algorithm    
  4. Kenjaev S. S., Akhatov A. R., Tajiev M. R. A Hybrid Combinational Approach to Sensitivity Quantification in Membership Function Selection during Fuzzification of Server Parameters 
  5. Perepelkin V.A., Arykov S.B. On Combining Active Knowledge Concept and Machine Learning     

V. N. Aleeva, M.P. Sokolov
South Ural State University (National Research University), 454080, Chelyabinsk, Russia

FORMATION OF REPRESENTATIONS OF ALGORITHMS FOR
SOFTWARE SYSTEMS BASED ON THE CONCEPT OF A Q-DETERMINANT

DOI: 10.24412/2073-0667-2026-1-5-23
EDN: EZZXDL
The Q-determinant concept is one approach to parallelizing numerical algorithms. It can be used to improve the efficiency of parallel computations by identifying and then utilizing algorithmic parallelism resources within a software system. Parallel programming technology was developed for this purpose. Research using the Q-determinant concept has demonstrated the feasibility of creating automated design and execution software systems for the efficient implementation of numerical algorithms. To describe algorithms, software systems must use algorithm representations in the form of Q-determinants. When solving practical problems, files containing algorithm representations in the form of Q-determinants can currently be large. Therefore, problems may arise when generating and using algorithm representations in the form of Q-determinants. In such cases, Q-determinants are called large, and the resulting problems are called large Q-determinant problems. This article describes the problems of large Q-determinants and proposes solutions.The paper continues the research based on the concept of the Q-determinant, which is the author’s approach to parallelization of numerical algorithms. There are described the following concepts of the Q-determinant concept used in research.

Key words: Q-determinant of algorithm, representation of algorithm in form of Q-determinant, Q-effective implementation of algorithm, parallelism resource of algorithm, Q-effective program, computer-aided design of effective programs.

References

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  2. Valentina Aleeva, Rifkhat Aleev. Investigation and Implementation of Parallelism Resources of Numerical Algorithms // ACM Transactions on Parallel Computing. 2023. Vol. 10. N 2, Article number 8. P. 1-64. DOI: 10.1145/3583755.
  3. Aleeva V. N. Podxod к e‘ffektivnoj realizacii cliislenny‘x algoritmov // Problemy1 informatiki. 2025. № 1. S. 29-44. DOI: 10.24412/2073-0667-2025-1-29-44 (in Russian).
  4. Aleeva V. N., Kuzneczov E.K. E‘ffektivnaya realizaciya algoritmov sortirovki s pomoshlPyu koncepcii Q-determinanta // Vestnik NGU. Seriya: Informacionny‘e texnologii. 2025. T. 23, № 2.
  5. S.    5-17. DOI: 10.25205/1818-7900-2025-23-2-5-17 (in Russian).
  6. Aleeva V. N., Sapozhnikov A.S. E‘ffektivnaya realizaciya algoritmov obucheniya nejronny‘x setej s pomoshh‘yu koncepcii Q-determinanta // Problemy1 informatiki. 2025. № 3. S. 5-16. DOI: 10.24412/2073-0667-2025-3-5-16 (in Russian).
  7. Aleeva V. N. Avtomatizirovannoe proektirovanie i ispolnenie e‘ffektivny‘x programm dlya chislenny‘x algoritmov // Vestnik YuUrGU. Seriya: Vy‘chislitePnaya matematika i informatika. 2023.
  8. T.    12, № 3. S. 31-49. DOI: 10.14529/cmse230303 (in Russian).
  9. Manatin P., Aleeva V. Efficient Implementation of Numerical Algorithms Based on a Lexical Analyzer // Parallel Computational Technologies. PCT 2024. Communications in Computer and Information Science. 2024. Vol. 2241. P. 107-121. DOI: 10.1007/978-3-031-73372-7_8.
  10. Aleeva V. N. Razrabotka programmny‘x sistem avtomatizirovannogo proektirovaniya i ispolneniya programm dlya effiektivnoj realizacii chislenny‘x algoritmov na osnove koncepcii Q- determinanta // Vestnik NGU. Seriya: Informacionny‘e texnologii. 2025. T. 23, № 1. S. 5-18. DOI: 10.25205/1818-7900-2025-23-1-5-18 (in Russian).
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  12. Aleeva V. N., Zotova P. S., Skleznev D.S. Rasshirenie vozmozhnostej issledovaniya resursa parallelizma chislenny‘x algoritmov s pomoshh‘yu programmnoj Q-sistemy‘ // Vestnik YuUrGU. Seriya: Vy‘chislitePnaya matematika i informatika. 2021. T. 10, № 2. S. 66-81. DOI: 10.14529/cmse210205 (in Russian).
  13. Aleeva V. N. Improving Parallel Computing Efficiency // Proceedings — 2020 Global Smart Industry Conference, GloSIC 2020. IEEE. 2020. P. 113-120. Article number 9267828. DOI: 10.1109/GloSIC50886.2020.9267828.
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Bibliographic reference:  Aleeva V. N., Sokolov M. P. Formation of Representations of Algorithms for Software Systems Based on the Concept of a Q-Determinant//"Problems of informatics",  2026, № 1, pp..5-23.  DOI: 10.24412/2073-0667-2026-1-5-23.
 

A. Vlasenko, M. Gorodnichev, M. Kurbatov*
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
Novosibirsk State Technical University, 630073, Novosibirsk, Russia
*Novosibirsk State University, 630090, Novosibirsk, Russia

DEBUGGING SYSTEM OF SIMPLE COMPUTATIONAL MODELS IN GRAPH REPRESENTATION

DOI: 10.24412/2073-0667-2026-1-24-39
EDN: NPOQMK
Computational models (CM) is a formalism for representing knowledge about computing in problem domains. A CM defines a set of domain quantities (variables) and a set of operations that functionally connect the quantities. The choice of subsets V (known variables) and W (desired variables) determines the formulation of the problem on the CM, and the partial order of operations that allows one to “compute” W by V is called a (U, W)-plan. With appropriate computer implementation of variables and operations, automated problem solving based on CMs becomes possible. Building a CM — as a theory of the problem domain — is a complex task that requires significant skills and experience.
It is convenient to represent a CM as a bipartite graph with vertices of two types: variables and operations. Some operations produce variable values as results that will be input for other operations.
There are several software systems for designing and using CMs (LuNA, HPC Community Cloud, CoCoViLa, Orlando Tools, etc.) These systems have different interfaces and the user experience varies significantly depending on the system. For example, in the HPC Community Cloud, a user can place elements corresponding to values and operations on a canvas in the web interface and link them with arrows. In the LuNA system, the user writes a program in the language of the same name, similar to functional languages.
When using such systems, the user can make a number of mistakes, both when developing a CM and when setting problems. As a result, the solutions to the problem may either not exist at all, or they may differ significantly depending on the choice of the (U, W)-plan.
The following are several types of situations that should be taken into account.
The CM-graph has several connectivity components. If the graph is large enough (several dozen or more vertices with many arcs), then this situation may be difficult to detect visually. The existence of several connectivity components may indicate that the modeled subject area should be divided into several independent areas and investigated separately.
The inability to calculate any variables from others. In many fields of physics, mathematics, and other sciences, all values are interconnected by formulas, and it is always possible to calculate any value through others. In this case, the presence of a variable that is not the result of any operation is an error in CM-development. Although there may be subject areas in which some variables are always only input and are not calculated through others.
This work was carried out under state contract with ICMMG SB RAS FWNM-2025-0005.
A number of possible (V, W)-plans for solving the problem. This situation may be normal, since often the same problem can be solved using different methods, but it may also indicate unnecessary connections that were mistakenly entered into the CM.
The computational model design system chooses an inefficient (V, W)-plan according to some criterion. For example, it was not taken into account that the computing system on which the task will be run has graphics accelerators; an inefficient method for solving a problem was chosen (for example, the Kramer method was chosen instead of an iterative method for solving a system of linear equations), etc.
When designing the CM, the limitations of the problem domain were not taken into account (for example, that a certain value cannot be negative, that the values are dependent on each other, etc.)
Therefore, it is necessary to develop a CM debugging system that performs a number of checks on the CM in an automated mode and is capable of analyzing the (V, W)-problems. This paper is devoted to the description of such a system.
The system under development receives a CM in the form of a JSON file with a description in a specific format (this format is described in the paper). At the moment, the user is downloading it from the file system. In the future, imports will be implemented directly from CM design systems. To do this, it is necessary to develop a parser for the internal CM representation of each of these systems. After import, the CM graph is displayed in the system's web interface. The user has the opportunity to set a (V, W)-problem by selecting the vertices of the sets V and W. In this case, all existing (V, W)- plans for this problem will be displayed on the screen. If there are no solutions to the problem in this CM, then this will be notified to the user. The system also detects the presence of several connectivity components of the CM graph.

Key words: computational model, high performance computing systems, bipartite graph, automated debugging, visualization.

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Bibliographic reference: Vlasenko A. Yu., Gorodnichev M.A., Kurbatov M.A. Debugging System of Simple Computational Models in Graph Representation//"Problems of informatics", 2026, № 1, pp..24-39.  DOI: 10.24412/2073-0667-2026-1-24-39.

A. R. Gerb, E. E. Deviatykh, G.A. Omarova
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
Novosibirsk State Universit, 630090, Novosibirsk, Russia

OPTIMIZATION OF THE k-SHORTEST PATHS ALGORITHM

DOI: 10.24412/2073-0667-2026-1-40-49
EDN: RGXRWO
This paper examines algorithms for finding k-shortest paths. An optimized algorithm for finding k-shortest simple (loop-free) paths in a directed graph is implemented. The algorithm is based on the ideas of the classical version of Yen’s algorithm and the reverse tree construction algorithm. Both implementations have complexity O(kn(m + n log n)).
Key words: graph, path, simple path, tree, graph algorithm, к shortest simple paths, space-time trade-off.
 

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Bibliographic reference: Gerb A.R., Deviatykh E. E., Omarova G. A. Optimization of the k-shortest Paths Algorithm //"Problems of informatics",  2026, № 1, pp..40-49.  DOI: 10.24412/2073-0667-2026-1-40-49.

S.S. Kenjaev, A. R. Akhatov, M.R. Tojiev
Samarkand State University, 703004, Samarkand, Uzbekistan

A HYBRID COMBINATIONAL APPROACH TO SENSITIVITY QUANTIFICATION IN MEMBERSHIP FUNCTION SELECTION
DURING FUZZIFICATION OF SERVER PARAMETERS

DOI: 10.24412/2073-0667-2026-1-50-64
EDN: YHQJXQ

In the process of efficiently managing request flows within information systems, accounting for the individual characteristics of servers plays a crucial role. Traditional load balancing algorithms- such as Round Robin, Weighted Round Robin, and regional distribution methods-typically allocate requests in a cyclic manner or based solely on predefined weight coefficients. These approaches fail to consider real-time server load levels, response speed, or operational state. This paper proposes a novel fuzzy logic-based model for request flow management, with particular attention given to the selection of appropriate membership functions for the linguistic representation of server parameters. During the fuzzification phase, the sensitivity of membership functions is quantified and optimized through a combinational hybrid approach. Experimental results demonstrate that the proper selection of membership functions enhances the accuracy of decision-making and reduces the degree of uncertainty. Consequently, the proposed approach significantly improves the flexibility, precision, and stability of request flow management in distributed server environments.
 

Key words: fuzzifiation, membership functions, sensitivity quantification, combinational hybrid approach, server load balancing, fuzzy logic, system reliability, adaptive control, linguistic modeling, request flow optimization, normalized sensitivity index, system.

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Bibliographic reference: Kenjaev S. S., Akhatov A. R., Tajiev M. R. A Hybrid Combinational Approach to Sensitivity Quantification in Membership Function Selection during Fuzzification of Server Parameters //"Problems of informatics", 2026, № 1, pp..50-64.  DOI: 10.24412/2073-0667-2026-1-50-64.

B.A. Перепелкин*, С. Б. Арыков**
Institute of computational mathematics and mathematical geophysics SB RAS, 630090, Novosibirsk, Russia
*Novosibirsk State University, 630090, Novosibirsk, Russia
**Novosibirsk State Technical University, 630073, Novosibirsk, Russia

ON COMBINING ACTIVE KNOWLEDGE CONCEPT AND MACHINE LEARNING

DOI: 10.24412/2073-0667-2026-1-65-78
EDN: YKXJIB
The problem of automatic program construction remains relevant in the context of continuously progressing computerization of all spheres of society. Despite significant achievements in automation tools such as compilers, programming languages, integrated development environments, and artificial intelligence methods, program construction largely remains a creative task that is difficult to automate. Universal approaches to automatic program construction that would produce sufficiently efficient programs for practical use within acceptable timeframes are algorithmically complex and have only niche applications. Therefore, it is important to explore and develop different approaches to automatic program construction and methodologies for their application and combination. In particular, it is valuable to utilize the experience of manual program development in various subject domains and create programming automation tools based on this experience.
This paper examines the active knowledge concept as one such approach and explores how it relates to and can be combined with machine learning methods. The active knowledge concept is a methodology for automatic program construction in specific subject domains. It is based on the theory of synthesis of parallel programs and systems on computational models [1]. The methodology enables automatic construction of sufficiently efficient programs for solving problems of a certain class within a particular subject domain, where efficiency is understood from the perspective of non-functional properties essential to that domain, such as execution time, memory consumption, network load, etc.
The fundamental principles of the active knowledge concept include non-universality, axiomatic theory as a foundation, partial description of the subject domain, use of computational models, multilevel construction, consideration of static and dynamic aspects, application to well-developed subject domains, inclusion of good solutions, variability, recommendations, alternative approach to program creation, accumulation of knowledge in active form, and instrumental support through systems like LuNA (Language for Numerical Algorithms). The LuNA system, developed and maintained at the Institute of Computational Mathematics and Mathematical Geophysics SB RAS, includes a language for describing active knowledge bases and a system for automatic construction and execution of parallel programs.
Machine learning methods, particularly those based on large language models, offer new opportunities for automating programming tasks. A practically widely used technology is the creation
This research was carried out under the state contract with ICM&MG SB RAS FWNM-2025-0005. 
of Al assistants — digital assistants capable of not only executing predefined commands but also understanding context and adapting their behavior accordingly. In software development, Al assistants can help with code generation, documentation, quality checking, education, and auxiliary technical tasks. Popular solutions include Cursor, Codex, GitHub Copilot, Gemini Code Assist, and domestic developments like SourceCraft Code Assistant and GigaCode.
This paper explores the potential synergies between the active knowledge concept and machine learning methods. Several principal possibilities for combining these approaches are considered: (1) An Al assistant for training and methodological support of LuNA system users, helping to overcome the entry barrier; (2) Al assistance in creating active knowledge bases, acting as a methodological consultant guiding users through key stages; (3) Automatic creation of active knowledge bases from human-oriented texts using machine learning; (4) Al translation from informal problem statements to formal specifications; (5) Improvement of active knowledge bases through analysis and optimization using large language models.
The paper presents a prototype implementation of an Al assistant for the LuNA system (LuNA Al), focused initially on documentation-related tasks to help overcome the entry barrier in learning and using the active knowledge concept. Technically, LuNA Al is a service that accepts context from the user (files, questions), combines this information with the available knowledge base (documentation, templates, examples), forms a prompt, calls a large language model, and displays the LLM’s response to the user.
The implementation utilizes Yandex Al Assistant API, which combines the YandexGPT large language model with RAG (Retrieval-Augmented Generation) technology for retrieving relevant information from knowledge bases. The system architecture includes a frontend application built with Vue and NuxtUI frameworks and a backend developed in Python with FastAPI. The user’s query is vectorized and, together with the most relevant context from the knowledge base, is fed to the I.LAI. For convenient updating of the knowledge base, the concept of a “project” is implemented at the UI level — a set of files forming a knowledge base, with support for multiple projects to maintain different versions of the LuNA system.
The current demonstration version of the Al assistant solves part of the documentation-related tasks: users can request information about the LuNA system, and the Al assistant builds relevant responses using RAG. Although the quality of responses currently requires further improvement, particularly in enhancing the knowledge base quality, even in this form the assistant can provide significant help to those newly acquainted with the LuNA language.
The research demonstrates that the active knowledge concept and machine learning methods have significant potential for combined use. Active knowledge bases, based on axiomatic theories, can serve as a flexible, rigorous mathematical apparatus allowing practically unlimited accumulation of knowledge that remains unchanged over time with the possibility of automatic application. Machine learning methods can rely on this apparatus, solving optimization problems within given axiomatic theories, as well as serving as a bridge to the informal human context.
Future work includes improving the quality of the knowledge base, integrating the Al assistant into popular development environments like VS Code, and expanding its functionality with additional capabilities such as code generation and optimization suggestions within the LuNA framework.
 

Key words: active knowledge concept, LuNA system, LLM, deep learning, Al assistant.

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Bibliographic reference:Perepelkin V.A., Arykov S.B. On Combining Active Knowledge Concept and Machine Learning  //"Problems of informatics",  2026, № 1, pp..65-78.  DOI: 10.24412/2073-0667-2026-1-65-78.