{"id":10289,"date":"2026-04-06T16:42:54","date_gmt":"2026-04-06T15:42:54","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=10289"},"modified":"2026-06-19T10:35:39","modified_gmt":"2026-06-19T09:35:39","slug":"25-6-7-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-7-en\/","title":{"rendered":"25.6.7 En"},"content":{"rendered":"\n

Software testing and mathematical error finding model<\/strong><\/h1>\n\n\n\n

I.V. Kuchumov<\/strong><\/p>\n\n\n\n

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Abstract<\/strong>.<\/strong> <\/em>Program testing is important to audit the quality of the program and its compliance with the initial specifications, reliability requirements, functionality, fullness of the complex, etc. Recently taking into account the compliance of the software product with consumer and market conditions is also relevant. This requires new approaches and methods, tools and technologies for verifying and testing programs in real code and real operation mode. This work is devoted to system analysis of testing environments and modeling of the debugging and testing process. Using general system methods (analysis-synthesis, composition-decomposition, modeling, etc.), mathematical modeling the following results were obtained: 1) an analysis of goals, types, testing methods was carried out; 2) classification of methods was carried out; 3) with certain initial hypotheses regarding the distribution of errors in the software system, a mathematical model for estimating the number of errors (vulnerabilities) in the software system, their dynamics using the apparatus of the class of ordinary differential equations «with saturation» was built and investigated. There are presented variants for development of problem statements (hypotheses), models, algorithms for identification of models for improvement of evidence and coverage of a wider class of test situations. Research results can be used for practical audit, control of the testing process.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/em><\/strong> testing, reliability, analysis, program, errors, mathematical model<\/p>\n\n\n\n

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For citation<\/strong>.<\/strong> Kuchumov I.V. Software testing and mathematical error finding model. News of the KabardinoBalkarian Scientific Center of RAS<\/em>. 2023. No. 6(116). Pp. 74\u201382. DOI: 10.35330\/1991-6639-2023-6-116-74-82<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Merzlyakova E.Yu., Yanchenko E.V. Review of verification methods and software quality assessment. Vestnik SibGUTI<\/em> [Bulletin of SibGUTI]. 2023. Vol. 17. No. 1. Pp. 92\u2013106. DOI:10.55648\/1998-6920-2023-17-1-92-106. (In Russian)<\/li>\n\n\n\n
  2. Ponachugin A.V. Software update in the structure of the modern information system. Kibernetika i programmirovaniye<\/em> [Cybernetics and programming]. 2019. \u2116 2. Pp. 65\u201372. DOI:10.25136\/2306-4196.2019.2.203413. (In Russian)<\/li>\n\n\n\n
  3. Lavrishcheva E.M., Zelenov S.V., Pakulin N.V. Methods for assessing the reliability of software and technical systems. Trudy ISP RAN <\/em>[Proceedings of ISP RAS]. 2019. Vol. 31. No. 5. Pp. 95\u2013108. DOI: 10.15514\/ISPRAS-2019-31(5)-7. (In Russian)<\/li>\n\n\n\n
  4. Shevchuk V.I. Pairwise testing of software. Universum: tekhnicheskiye nauki <\/em>[Universum: Technical sciences]. 2023. No. 7(112). DOI: 10.32743\/UniTech.2023.112.7.15767. (In Russian)<\/li>\n\n\n\n
  5. Kashkevich A.M., Badanina Yu.V., Filimonov A.S., Dolgikh A.I. Verification of software systems using the example of a statically determinate prismatic beam. Izvestiya VUZov (ser. \u201cMashinostroyeniye\u201d) <\/em>[Higher education institutions news («Mechanical Engineering»)]. 2023. No. 5. Pp. 29\u201336. DOI:10.18698\/0536-1044-2023-5-29-36. (In Russian)<\/li>\n\n\n\n
  6. Radionova Yu.A., Savkin A.L. Construction of a model for forecasting peak loads of a working process based on time series analysis. Avtomatizatsiya protsessov upravleniya<\/em> [Automation of control processes]. 2020. No. 2(60). Pp. 53\u201360. DOI: 10.35752\/1991-2927-2020-2-60-53-61. (In Russian)<\/li>\n\n\n\n
  7. Maksimov M.I., Gorina E.A. Agile methodology as a driver of effective corporate culture. Regional’naya i otraslevaya ekonomika<\/em> [Regional and industrial economics]. 2023. No. 1. Pp. 102\u2013111. DOI:10.47576\/2949-1916_2023_1_102. (In Russian)<\/li>\n\n\n\n
  8. Samarin N.N. A model for the safe functioning of software that formalizes control of memory use and processor access to it. Naukoyemkiye tekhnologii v kosmicheskikh issledovaniyakh Zemli <\/em>[Science-intensive technologies in space research of the Earth]. 2021. Vol. 13. No. 1. Pp. 68\u201379. DOI:10.36724\/2409-5419-2021-13-1-68-79. (In Russian)<\/li>\n\n\n\n
  9. Shakirova A.I., Khasyanov A.F., Dautov E.F. Reducing the time of software testing. Sovremennyye naukoyemkiye tekhnologii <\/em>[Modern science-intensive technologies]. 2019. No. 7. Pp. 104\u2013109. (In Russian)<\/li>\n\n\n\n
  10. Goryainov V.B., Goryainova E.R. Comparison of maximum likelihood estimates and least modules of autoregression process parameters with random coefficients. Vestnik MGTU im. N.E. Baumana (ser. \u201cYestestvennyye nauki\u201d)<\/em> [Bulletin of the Bauman Moscow State Technical University (ser. \u201cNatural Sciences\u201d)]. 2015. No. 3. Pp. 20\u201330. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
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    Kuchumov Ilya Vadimovich<\/strong>, Head of the Development Department, Yandex company;
    119021, Russia, Moscow, 16 Lev Tolstoy street;
    kuchumov.ilya@gmail.com; ORCID: https:\/\/orcid.org\/0009-0003-6470-5587<\/p>\n\n\n\n


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    Software testing and mathematical error finding model I.V. Kuchumov Abstract. Program testing is important to audit the quality of the program and its compliance with the initial specifications, reliability requirements, functionality, fullness of the complex, etc. Recently taking into account the compliance of the software product with consumer and market conditions is also relevant. This […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-10289","page","type-page","status-publish","hentry"],"yoast_head":"\n25.6.7 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-7-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.6.7 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Software testing and mathematical error finding model I.V. 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