{"id":10305,"date":"2026-04-06T16:52:55","date_gmt":"2026-04-06T15:52:55","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=10305"},"modified":"2026-04-10T08:10:28","modified_gmt":"2026-04-10T07:10:28","slug":"25-6-15-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/25-6-15-en\/","title":{"rendered":"25.6.15 En"},"content":{"rendered":"\n

On finding an estimate of the complexity of discrete k-valued functions<\/strong><\/h1>\n\n\n\n

D.P. Dimitrichenko<\/strong><\/p>\n\n\n\n

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Abstract<\/strong>:<\/strong> <\/em>In this paper the concept of derivative and integral of discrete k-valued functions is introduced, taking into account the properties of the operations of addition and multiplication modulo k. Based on the property of completeness of the integral expansion of k-valued functions, a universal method is proposed for estimating the complexity of k-valued fully defined functions, including not having an analytical representation, but specified only in a tabular way, or representable using other tabular functions. The structure of the \u201cprimitive \u2013 derivative\u201d relation is studied depending on the properties of the number k. A model in the form of a directed graph of this relationship is proposed. Three main types of introduced relations are identified.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/em><\/strong> k-valued function, differentiation operator, integration operator, completeness property, integral basis functions, directed graph<\/p>\n\n\n\n

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For citation<\/strong>.<\/strong> Dimitrichenko D.P. On finding an estimate of the complexity of discrete k-valued functions. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2023. No. 6(116). Pp. 142\u2013151. DOI: 10.35330\/1991-6639-2023-6-116-142-151<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Gorbatov V.A. Fundamental’nyye osnovy diskretnoy matematiki<\/em> [Fundamental foundations of discrete mathematics]. Moscow: Nauka, 2000. 544 p. (In Russian)<\/li>\n\n\n\n
  2. Panteleev V.I. Polynomial decomposition of K-valued functions by Differentiation and normalization operators. Izvestiya vysshikh uchebnykh zavedeniy: Matematika<\/em> [News of higher educational institutions: Mathematics]. 1998. No. 1. Pp. 82\u2013103. (In Russian)<\/li>\n\n\n\n
  3. Lyutikova L.A. Using a Boolean derivative to evaluate the significance of properties of recognized objects. E3S Web of Conferences 224. 01021 (2020).<\/li>\n\n\n\n
  4. Kostrykin A.I. Vvedeniye v algebru<\/em> [Introduction to algebra]. Moskow: Nauka, 1977. 320 p. (In Russian)<\/li>\n\n\n\n
  5. Dimitrichenko D.P. On one way of differentiating logical functions. Materialy mezhdunarodnoy konferentsii molodykh uchenykh \u201cMatematicheskoye modelirovaniye fraktal’nykh protsessov, rodstvennyye problemy analiza i informatiki\u201d<\/em> [Proceedings of the international conference of young scientists \u201cMathematical modeling of fractal processes, related problems of analysis and computer science\u201d]. Nalchik, 2011. Pp. 103\u2013105. (In Russian)<\/li>\n\n\n\n
  6. Dimitrichenko D.P. On the representation of a logical function through its derivatives. Materialy II mezhdunarodnogo rossiysko-uzbekskogo simpoziuma \u00abUravneniya smeshannogo tipa i smezhnyye problemy analiza i informatiki\u00bb<\/em> [Materials of the II International Russian-Uzbek Symposium \u201cEquations of mixed type and related problems of analysis and computer science\u201d]. Nalchik, 2012. Pp. 92\u201394. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
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    Dimitrichenko Dmitry Petrovich<\/strong>, Candidate of Technical Sciences, Senior Researcher of the Department of Neuroinformatics and Machine Learning, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    360000, Russia, Nalchik, 89 A Shortanov street;
    dimdp@rambler.ru, ORCID: https:\/\/orcid.org\/0000-0003-2399-3538<\/p>\n\n\n\n

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    On finding an estimate of the complexity of discrete k-valued functions D.P. Dimitrichenko Upload the full text Abstract: In this paper the concept of derivative and integral of discrete k-valued functions is introduced, taking into account the properties of the operations of addition and multiplication modulo k. Based on the property of completeness of the […]<\/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-10305","page","type-page","status-publish","hentry"],"yoast_head":"\n25.6.15 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\/25-6-15-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"25.6.15 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=\"On finding an estimate of the complexity of discrete k-valued functions D.P. 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