{"id":3521,"date":"2025-02-21T14:26:00","date_gmt":"2025-02-21T11:26:00","guid":{"rendered":"http:\/\/selftiming.ru\/new\/?p=3521"},"modified":"2025-12-16T14:58:15","modified_gmt":"2025-12-16T11:58:15","slug":"mathematical-models-of-critical-soft-error-in-synchronous-and-self-timed-pipeline","status":"publish","type":"post","link":"http:\/\/selftiming.ru\/new\/2025\/02\/21\/mathematical-models-of-critical-soft-error-in-synchronous-and-self-timed-pipeline\/","title":{"rendered":"Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline"},"content":{"rendered":"\n<p>Igor Sokolov, Yuri Stepchenkov, Yuri Diachenko and Dmitri Khilko. Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline \/\/ Mathematics, 2025. 13(5):695, 15 p.<\/p>\n\n\n\n<p>DOI:10.3390\/math13050695 \u0418\u043d\u0434. \u0432 \u044f\u0434\u0440\u0435 \u0420\u0418\u041d\u0426, \u0411\u0421 \u041a1, Scopus Q2, WoS Q1. URL: <a rel=\"noreferrer noopener\" href=\"https:\/\/www.mdpi.com\/2227-7390\/13\/5\/695\" target=\"_blank\">https:\/\/www.mdpi.com\/2227-7390\/13\/5\/695<\/a>, EID: 2-s2.0-86000738193, <em>Part of<\/em> ISSN: <a rel=\"noreferrer noopener\" href=\"https:\/\/portal.issn.org\/resource\/ISSN\/2227-7390\" target=\"_blank\">22277390<\/a><\/p>\n\n\n\n<p><strong>\u0424\u0438\u043d\u0430\u043d\u0441\u043e\u0432\u0430\u044f \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0430:<\/strong> \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e \u043f\u0440\u0438 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0435 \u041c\u0438\u043d\u0438\u0441\u0442\u0435\u0440\u0441\u0442\u0432\u0430 \u041d\u0430\u0443\u043a\u0438 \u0438 \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f \u0420\u043e\u0441\u0441\u0438\u0439\u0441\u043a\u043e\u0439 \u0424\u0435\u0434\u0435\u0440\u0430\u0446\u0438\u0438, \u043f\u0440\u043e\u0435\u043a\u0442 \u2116 075-15-2024-544 \/ <strong>Funding Agency<\/strong>: This research was supported by the Ministry of Science and Higher Education of the Russian Federation, project No 075-15-2024-544.<\/p>\n\n\n\n<p><strong>Abstract:<\/strong> This paper analyzes the impact of a single soft error on the performance of a synchronous and self-timed pipeline. A nuclear particle running through the integrated circuit body is considered the most probable soft error source. The existing estimates show that self-timed circuits offer an advantage in terms of single soft error tolerance. The paper proves these estimates on the basis of a comparative probability analysis of a critical fault in two types of pipelines. The mathematical models derived in the paper describe the probability of a critical fault depending on the circuit\u2019s characteristics, its operating discipline, and the soft error parameters. The self-timed pipeline operates in accordance with a two-phase discipline, based on the request\u2013acknowledge interaction within the pipeline\u2019s stages, which provides it with increased immunity to soft errors. Quantitative calculations performed on the basis of the derived mathematical models show that the self-timed pipeline has about 6.1 times better tolerance to a single soft error in comparison to its synchronous counterpart. The obtained results are in good agreement with empirical estimates of the soft error tolerance level of synchronous and self-timed circuits.<\/p>\n\n\n\n<p><strong>\u0410\u043d\u043d\u043e\u0442\u0430\u0446\u0438\u044f:<\/strong> \u0421\u0442\u0430\u0442\u044c\u044f \u0430\u043d\u0430\u043b\u0438\u0437\u0438\u0440\u0443\u0435\u0442 \u0432\u043b\u0438\u044f\u043d\u0438\u0435 \u043e\u0434\u0438\u043d\u043e\u0447\u043d\u043e\u0433\u043e \u043b\u043e\u0433\u0438\u0447\u0435\u0441\u043a\u043e\u0433\u043e \u0441\u0431\u043e\u044f \u043d\u0430 \u0440\u0430\u0431\u043e\u0442\u043e\u0441\u043f\u043e\u0441\u043e\u0431\u043d\u043e\u0441\u0442\u044c \u0441\u0438\u043d\u0445\u0440\u043e\u043d\u043d\u043e\u0433\u043e \u0438 \u0441\u0430\u043c\u043e\u0441\u0438\u043d\u0445\u0440\u043e\u043d\u043d\u043e\u0433\u043e (\u0421\u0421) \u043a\u043e\u043d\u0432\u0435\u0439\u0435\u0440\u0430. \u0412 \u043a\u0430\u0447\u0435\u0441\u0442\u0432\u0435 \u043d\u0430\u0438\u0431\u043e\u043b\u0435\u0435 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Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline \/\/ Mathematics, 2025. 13(5):695, 15 p. DOI:10.3390\/math13050695 \u0418\u043d\u0434. \u0432 \u044f\u0434\u0440\u0435 \u0420\u0418\u041d\u0426, \u0411\u0421 \u041a1, Scopus Q2, WoS Q1. URL: https:\/\/www.mdpi.com\/2227-7390\/13\/5\/695, EID: 2-s2.0-86000738193, Part of ISSN: 22277390 \u0424\u0438\u043d\u0430\u043d\u0441\u043e\u0432\u0430\u044f \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0430: \u0418\u0441\u0441\u043b\u0435\u0434\u043e\u0432\u0430\u043d\u0438\u0435 \u0432\u044b\u043f\u043e\u043b\u043d\u0435\u043d\u043e \u043f\u0440\u0438 \u043f\u043e\u0434\u0434\u0435\u0440\u0436\u043a\u0435 \u041c\u0438\u043d\u0438\u0441\u0442\u0435\u0440\u0441\u0442\u0432\u0430 \u041d\u0430\u0443\u043a\u0438 \u0438 \u041e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u044f [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[65,54,1,12,53,59],"tags":[],"class_list":["post-3521","post","type-post","status-publish","format-standard","hentry","category-65","category-dyachenko-yu-g","category-publications","category-samosinhronnaya-shemotehnika","category-stepchenkov-yu-a","category-hilko-d-v"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.0 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline - \u041f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0435 \u043f\u0443\u0442\u0438 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0430\u043f\u043f\u0430\u0440\u0430\u0442\u0443\u0440\u044b<\/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:\/\/selftiming.ru\/new\/2025\/02\/21\/mathematical-models-of-critical-soft-error-in-synchronous-and-self-timed-pipeline\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline - \u041f\u0435\u0440\u0441\u043f\u0435\u043a\u0442\u0438\u0432\u043d\u044b\u0435 \u043f\u0443\u0442\u0438 \u0440\u0435\u0430\u043b\u0438\u0437\u0430\u0446\u0438\u0438 \u0430\u043f\u043f\u0430\u0440\u0430\u0442\u0443\u0440\u044b\" \/>\n<meta property=\"og:description\" content=\"Igor Sokolov, Yuri Stepchenkov, Yuri Diachenko and Dmitri Khilko. Mathematical models of Critical Soft Error in Synchronous and Self-Timed Pipeline \/\/ Mathematics, 2025. 13(5):695, 15 p. DOI:10.3390\/math13050695 \u0418\u043d\u0434. \u0432 \u044f\u0434\u0440\u0435 \u0420\u0418\u041d\u0426, \u0411\u0421 \u041a1, Scopus Q2, WoS Q1. 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