Abstract
We consider the synthesis problem of two-pole contact circuits implementing given Boolean functions and admitting short fault detection test with respect to contact breaks. For each n-place Boolean function, we found the smallest possible lengths of the single and complete fault detection tests. In particular, it is shown that such length are not greater than n.
Originally published in Diskretnaya Matematika (2017) 29,№4, 66–86 (in Russian).
funding
This research was carried out with the financial support of the Russian Science Foundation (RSF) grant 14-21-00025 P.
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 of control of work of electric schemes”, Trudy Mat. Inst. Steklov., 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 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] Madatyan Kh. A., “Full test for repeating contact schemes”, Problemy kibernetiki, M.: Nauka, 1970, 103–118 (in Russian).Search in Google Scholar
[7] Reďkin N. P., “On complete checking tests for contact circuits”, Metody diskretnogo analiza v optimizatsii upravlyayushchikh system, Izd-vo IM SO AN SSSR, Novosibirsk, 1983, 80–87 (in Russian).Search in Google Scholar
[8] Reďkin N. P., “On checking tests of closure and opening”, Metody diskretnogo analiza v optimizatsii upravlyayushchikh sistem, Izd-vo IM SO AN SSSR, Novosibirsk, 1983, 87–99 (in Russian).Search in Google Scholar
[9] 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
[10] 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
© 2018 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics
Articles in the same Issue
- Frontmatter
- Estimate of the maximal cycle length in the graph of polynomial transformation of Galois–Eisenstein ring
- Durfee squares in compositions
- On fault detection tests of contact break for contact circuits
- On the number of integer points in a multidimensional domain
- On Stone’s renewal theorem for arithmetic distributions
- Local limit theorems for one class of distributions in probabilistic combinatorics