Abstract
We identify the classes of Boolean functions that may be implemented by easily testable circuits in the Zhegalkin basis for constant type-1 faults on outputs of gates. An upper estimate for the length of a complete fault detection test for three-place functions is obtained.
References
[1] Lupanov O. B., Asymptotic estimates of the complexity of control systems, Moscow State Univ., Moscow, 1984 (in Russian).Search in Google Scholar
[2] Yablonsky S. V., Introduction to Discrete Mathematics, Vysshaya Shkola, Moscow, 2002 (in Russian).Search in Google Scholar
[3] Yablonskii S. V., “Some questions of reliability and checking of control systems”, Mathematical Problems of Cybernetics, 1 (1988), 5–25 (in Russian).Search in Google Scholar
[4] Redkin N. P., Reliability and Diagnosis of Circuits, Moscow State Univ. Press, Moscow, 1992 (in Russian).Search in Google Scholar
[5] Borodina Yu. V., Borodin P. A., “Synthesis of easily testable circuits over the Zhegalkin basis in the case of constant faults of type 0 at outputs of elements”, Discrete Math. Appl., 20:4 (2010), 441–449.10.1515/dma.2010.027Search in Google Scholar
[6] Borodina Yu. V., “Easily testable circuits in Zhegalkin basis in the case of constant faults of type “1” at gate outputs”, Discrete Math. Appl., 30:5 (2020), 303–306.10.1515/dma-2020-0026Search in Google Scholar
[7] Romanov D. S., “A method of synthesis of irredundant circuits in the Zhegalkin basis admitting single fault diagnostic test sets with cardinality 1”, Izv. VUZov. Povolzhskiy region. Fiziko-matematicheskie nauki, 4 (36) (2015), 38–54.Search in Google Scholar
[8] Romanov D. S., Romanova E. Yu., “A method of synthesis of irredundant circuits admitting single fault detection tests of constant length”, Discrete Math. Appl., 29:1 (2019), 35–48.10.1515/dma-2019-0005Search in Google Scholar
[9] Popkov K.A., “A method for constructing logic networks allowing short single diagnostic tests”, Prikl. Diskr. Matem., 46 (2019), 38–57 (in Russian).10.17223/20710410/46/4Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Some classes of easily testable circuits in the Zhegalkin basis
- On the concentration of the independence numbers of random hypergraphs
- On implementation of some systems of elementary conjunctions in the class of separating contact circuits
- Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
- Maximally nonlinear functions over finite fields
- The limit joint distributions of statistics of four tests of the NIST package
Articles in the same Issue
- Frontmatter
- Some classes of easily testable circuits in the Zhegalkin basis
- On the concentration of the independence numbers of random hypergraphs
- On implementation of some systems of elementary conjunctions in the class of separating contact circuits
- Local limit theorem for the number of empty cells in a scheme of random equiprobable allocations
- Maximally nonlinear functions over finite fields
- The limit joint distributions of statistics of four tests of the NIST package