On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
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Dmitry V. Zakablukov
Abstract
The paper is concerned with the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates under constraints on the number of additional inputs. We study the Shannon functions for the complexity L(n, q) and depth D(n, q) of a reversible circuit implementing a map
Note: Originally published in Diskretnaya Matematika (2020) 32, №1, 8–26 (in Russian).
Funding statement: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 16-01-00196 A)
References
[1] Shannon C. E., “The synthesis of two-terminal switching circuits”, Bell System Tech. J., 28:8 (1949), 59–98.10.1002/j.1538-7305.1949.tb03624.xSearch in Google Scholar
[2] Yablonskiy S. V., Introduction to Discrete Mathematics, Nauka, M., 1986 (in Russian), 384 pp.Search in Google Scholar
[3] Lupanov O. B., “On a method of synthesis of circuits”, Izv. vuzov. Radiofizika, 1:1 (1958), 23–26 (in Russian).Search in Google Scholar
[4] Lupanov O. B., “On the schemes from functional elements with delays”, Problemy kibernetiki, vyp. 23, Nauka, M., 1970, 43–81 (in Russian).Search in Google Scholar
[5] Karpova N. A., “On computations with limited memory”, Matematicheskie voprosy kibernetiki, vyp. 2, Nauka, M., 1989, 131–144 (in Russian).Search in Google Scholar
[6] Feynman R., “Quantum mechanical computers”, Optic News, 11:2 (1985).10.1364/CLEO.1984.TUAA2Search in Google Scholar
[7] Maslov D. A., Reversible Logic Synthesis, Ph. D. Thesis, 2003, 165 pp.Search in Google Scholar
[8] Shende V. V., Prasad A. K., Markov I. L., Hayes J. P., “Synthesis of reversible logic circuits”, IEEE Trans. Computer-Aided Des. of Integr. Circuits and Systems, 22:6 (2006), 710–722.10.1109/TCAD.2003.811448Search in Google Scholar
[9] Zakablukov D. V., “On the gate complexity of reversible circuits consisting of NOT, CNOT and 2-CNOT gates”, Discrete Math. Appl., 27:1 (2017), 57–67.10.1515/dma-2017-0007Search in Google Scholar
[10] Zakablukov D. V., “Estimation of the depth of reversible circuits consisting of NOT, CNOT and 2-CNOT gates”, Moscow Univ. Math. Bull., 71:3 (2016), 89-97.10.3103/S0027132216030013Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
Articles in the same Issue
- Frontmatter
- Reduction of the integer factorization complexity upper bound to the complexity of the Diffie–Hellman problem
- Pseudo orthogonal Latin squares
- Panchromatic colorings of random hypergraphs
- On the connectivity of configuration graphs
- Asymptotics with remainder term for moments of the total cycle number of random A-permutation
- On the dependence of the complexity and depth of reversible circuits consisting of NOT, CNOT, and 2-CNOT gates on the number of additional inputs
- Letter to the Editor
