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Bounds on Shannon functions of lengths of contact closure tests for contact circuits

  • Kirill A. Popkov EMAIL logo
Published/Copyright: June 25, 2021

Abstract

We consider the problem of synthesis of irredundant two-pole contact circuits which implement n-place Boolean functions and allow short single fault detection or diagnostic tests of closures of at most k contacts. We prove that the Shannon function of the length of a fault detection test is equal to n for any n and k, and that the Shannon function of the length of a diagnostic test is majorized by n + k(n − 2) for n ⩾ 2.


Originally published in Diskretnaya Matematika (2020) 32,№3, 49–67 (in Russian).


References

[1] Lupanov O.B., Asymptotic bounds on complexity of control systems, M.: Izd-vo Mosk. un-ta, 1984 (in Russian), 138 pp.Search in Google Scholar

[2] Chegis I. A., Yablonskii S. V., “Logical methods for control of electric circuits”, Tr. MIANSSSR, 51 (1958), 270-360 (in Russian).Search in Google Scholar

[3] Yablonskiy S. V., “Reliability and control systems monitoring”, Materialy Vsesoyuznogo seminara po diskretnoy matematike i eeprilozheniyam, M.: Izd-vo Mosk. un-ta, 1986,7-12 (in Russian).Search in Google Scholar

[4] Yablonskiy S. V., “Some problems of reliability and monitoring of control systems”, Matematicheskie voprosy kiber netiki, M.: Nauka, 1988,5-25 (in Russian).Search in Google Scholar

[5] Red'kin N. P., Reliability and diagnostics schemes, M.: Izd-vo Mosk. un-ta, 1992 (in Russian), 192 pp.Search in Google Scholar

[6] Popkov K. A., “On diagnostic tests of contact break for contact circuits”, Discrete Math. Appl., 30:2 (2020), 103-116.10.1515/dma-2020-0010Search in Google Scholar

[7] Madatyan Kh. A., “Complete test for non-repeating contact circuits”, Problemy kibernetiki, Nauka, Moscow, 1970, 103-118 (in Russian).Search in Google Scholar

[8] Red'kin N. P., “On complete fault detection tests for contact circuits”, Metody diskretnogo analiza v issledovanii ekstrmal'nykh struktur, Izd-vo IM SO AN SSSR, Novosibirsk, 1983,80-87 (in Russian).Search in Google Scholar

[9] Red'kin N. P., “On checking tests of closure and opening”, Metody diskretnogo analiza v optimizatsii upravlyayushchikh sis- tem, Vyp. 40, IM SO AN SSSR, Novosibirsk, 1983, 87-99 (in Russian).Search in Google Scholar

[10] Romanov D. S., “On the synthesis of contact circuits that allow short fault detection tests”, Uchenye zapiski Kazanskogo universiteta. Fiziko-matematicheskie nauki, 156:3 (2014), 110-115 (in Russian).Search in Google Scholar

[11] Romanov D. S., Romanova E. Yu., “Single fault detection tests for generalized iterative switching circuits”, Moscow Univ. Comput. Math. Cyber., 2015, N 39,144-152.10.3103/S0278641915030073Search in Google Scholar

[12] Popkov K. A., “Tests of contact closure for contact circuits”, Discrete Math. Appl., 26:5 (2016), 299-308.10.1515/dma-2016-0025Search in Google Scholar

[13] Popkov K. A., “On fault detection tests of contact break for contact circuits”, Discrete Math. Appl., 28:6 (2018), 369-383.10.1515/dma-2018-0033Search in Google Scholar

[14] Popkov K. A., “Short single fault detection tests for contact circuits under breaks and closures of contacts”, Intelligent systems. Theory and applications, 23:3 (2019), 97-130 (in Russian).Search in Google Scholar

[15] Popkov K. A., “Short tests of closures for contact circuits”, Math. Notes, 107:4 (2020), 653-662.10.1134/S0001434620030323Search in Google Scholar

[16] Popkov K. A., “On complete diagnostic tests for contact circuits during opening and/or closing of contacts”, Izv. VUZ'ov. Povolzhskiy region. Fiz.-matem. nauki, 2019, N 3 (51), 3-24 (in Russian).10.21685/2072-3040-2019-3-1Search in Google Scholar

[17] Yablonsky S.V., Introduction to Discrete Mathematics, M.: Nauka, 1986 (in Russian), 384 pp.Search in Google Scholar

[18] Lozhkin S. A., Lectures on the Foundations of Cybernetics, Moscow, VMK Mosk. Gos. Univ., 2004 [in Russian]. (in Russian).Search in Google Scholar

Received: 2019-12-27
Published Online: 2021-06-25
Published in Print: 2021-06-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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