The possible copying of parts of code in the solution by participants in educational programming courses makes it difficult to objectively estimate the level of knowledge of each student. The article describes a solution to this problem using the example of the author's digital educational platform Mirera. The requirements for anti-plagiarism tool which take the specifics of the digital educational platform Mirera into account are set. Algorithms and methods for anti-plagiarism are considered, their advantages and disadvantages are highlighted. The details of the implementation of the fingerprinting method on a tokenized program and examples of the work of anti-plagiarism tool are described. The possibility of using the tool as an instrument for better understanding the students and the degree of mastering the course is noted.

The article describes research on the possibility of recognizing children's emotions based on convolutional neural networks for use in digital educational environments such as, PiktoMir. Alternative solutions are considered and the experience of creating your own neural network trained on an experimental data set is presented. The results of testing the system using various metrics based on the validation data set and comparing the results with the most popular emotion recognition algorithms are presented. Conclusions are drawn on the direction of further research, in particular, the need to expand the training data set, further steps are proposed for refinement in order to integrate into the PiktoMir educational environment.

In our country, the process of digital transformation of education is actively underway, which puts forward the requirements for the creation of digital educational platforms that provide reliable access to a variety of digital educational resources. Such platforms are essentially distributed computing systems. The importance and criticality of the tasks performed by digital educational resources determine the high level of technical requirements for the platforms on which they are implemented. The article considers the criteria that ensure the reliability of platforms, analyzes the existing popular solutions in the field of ensuring the reliability of digital educational platforms, and analyzes the compliance of these solutions with the specified criteria. It is shown that the existing digital educational platforms are generally far from meeting the set requirements. The authors proposed a variant of a digital educational platform that meets the formulated criteria.

The interaction between a teacher and a student reaches a new level of collaboration when using educational platforms: learning becomes faster and more efficient. However, at the same time, many routine processes remain that make the work of the teacher difficult, such as, for example, recording student attendance. Attendance control should be carried out by the teacher, regardless of whether the lesson is held in person or remotely. The solution to this problem should have a certain convenience both for the teacher, minimizing the time spent on registering those present at the lesson, and for the students themselves. The article proposes a solution to this problem on the example of Mirer's author's digital educational platform. The possibility of using such a mechanism to increase the involvement of students in the learning process is noted.

Spreadsheets are successfully used in many areas of the economy, finance, business, etc. In order for schoolchildren and students to gain competencies in working with spreadsheets, it was decided to add the ability to use spreadsheet tasks in courses to Mirera's digital educational platform, for which a corresponding author's module was created. The study of spreadsheets is defined by the Federal State Educational Standard for Informatics of the main school, tasks for the use of spreadsheets are included in the state final tests of schoolchildren. The developed module fully covers the required amount of familiarity with spreadsheets and allows you to create contests in automated verification in Mirera's digital educational platform without installing any additional software on the student's computer.

Courses in computer science and information and communication technologies can include a wide range of topics from the basics of programming and elementary knowledge about the structure of computers to the theory of formal grammars, artificial intelligence languages, operating systems, 3D graphics, etc. The main difficulty in this case is the mathematical component of the courses, which requires appropriate training of students. However, in programming there is content that is quite difficult for students to understand, even with deep academic knowledge. This area is parallel programming, when, on the one hand, it is required to study and write educational highly efficient algorithms for solving problems for performing simultaneous calculations on different computers or processors, on the other hand, it is no less difficult to understand - ensuring the parallel operation of various parts of a program with a shared access to shared data. The development of the latter is complicated by the lack of adequate visualization of the parallel operation of processes on a computer. It remains for teachers to illustrate the topic with pictures from the real world, giving various arguments to prove the importance of solving the problem of sharing common resources, citing, as one of the options, the simultaneous free moving of four cars at a crossroad. On the other hand, current trends require lowering the age of the beginning of acquaintance with the elements of programming and algorithmization. Preschoolers, children of the fourth year of life, successfully master the basic concepts of sequential programming using program-controlled robots and their virtual counterparts in the digital educational environment PiktoMir. The same DEE PiktoMir is used for programming propaedeutics in teaching for all ages, including university students. PiktoMir is not only easy to learn, but allows the use of several robot performers in tasks at the same time, each of which acts according to its own program. The visibility of the program execution process in the system led the authors to the idea of using the DEE PiktoMir to demonstrate the operation of classical mutual exclusion algorithms in courses on parallel programming. The experience of the authors showed the high efficiency of this approach, which allowed students to understand the problem in a short time and successfully solve all the problems of the course. This approach was tested in the courses Operating Systems (IIS SUM) and Algorithms and Data Structures (Institute of Childhood, Moscow State Pedagogical University).

The DSSP-TVM software complex created at the Research Laboratory of Ternary Informatics at the Faculty of Computational Mathematics and Cybernetics of Moscow State University can be used as an environment for developing and running programs for a ternary computer. Initially, it provided only operations of integer arithmetic. Then the DSSP-TVM was supplemented with a package of real floating point arithmetic operations. Now a package of complex arithmetic has been created on its basis. The article describes the main possibilities of the proposed package, as well as explains the most important aspects of its implementation in the DSSP-T language in the environment of the DSSP/TVM interpreter.

Bettin, D. Koukoulopuos and C. Sanna proved in 2021 that the set of products of two arbitrary sets of integer with unit density is again a set with density of one. Article 3 of the authors also provides the top grades for the so-called corresponding complement sets under some special constraints. This article provides similar estimates for weaker restrictions.