On diagnostic tests of contact break for contact circuits
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Kirill A. Popkov
Abstract
We prove that, for n ⩾ 2, any n-place Boolean function may be implemented by a two-pole contact circuit which is irredundant and allows a diagnostic test with length not exceeding n + k(n − 2) under at most k contact breaks. It is shown that with k = k(n) ⩽ 2n−4, for almost all n-place Boolean functions, the least possible length of such a test is at most 2k + 2.
Note: Originally published in Diskretnaya Matematika (2019) 31, №2, 123–142 (in Russian).
Funding: This research was carried out with the support of the program 01 “Fundamental Mathematics and its Applications” of the Presidium of the Russian Academy of Sciences (grant PRAS-18-01).
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. MIAN SSSR, 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 ee prilozheniyam, 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 kibernetiki, M.: Nauka, 1988, 5–25 (in Russian).Search in Google Scholar
[5] Reďkin N. P., Reliability and diagnostics schemes, M.: Izd-vo Mosk. un-ta, 1992 (in Russian), 192 pp.Search in Google Scholar
[6] Kolyada S. S., Upper bounds for the length of validation tests for circuits of functional elements, Diss. na soisk. uch. st. k.f.-m.n., Moscow, 2013 (in Russian), 77 pp.Search 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] Reďkin N. P., “On complete fault detection tests for contact circuits”, Metody diskretnogo analiza v issledovanii ekstrmaľnykh struktur, Izd-vo IM SO AN SSSR, Novosibirsk, 1983, 80–87 (in Russian).Search in Google Scholar
[9] Reďkin N. P., “On checking tests of closure and opening”, Metody diskretnogo analiza v optimizatsii upravlyayushchikh sistem, 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] 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
[12] 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
[13] Yablonskiy S. V., Introduction to Discrete Mathematics, Nauka, Moscow, 1986 (in Russian), 384 pp.Search in Google Scholar
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Articles in the same Issue
- On a method of synthesis of correlation-immune Boolean functions
- On the Δ-equivalence of Boolean functions
- On diagnostic tests of contact break for contact circuits
- On stabilization of an automaton model of migration processes
- Bounds on the discrepancy of linear recurring sequences over Galois rings
- Asymptotically best method for synthesis of Boolean recursive circuits
Articles in the same Issue
- On a method of synthesis of correlation-immune Boolean functions
- On the Δ-equivalence of Boolean functions
- On diagnostic tests of contact break for contact circuits
- On stabilization of an automaton model of migration processes
- Bounds on the discrepancy of linear recurring sequences over Galois rings
- Asymptotically best method for synthesis of Boolean recursive circuits
