Home On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs
Article
Licensed
Unlicensed Requires Authentication

On synthesis of reversible circuits consisting of NOT, CNOT, 2-CNOT gates with small number of additional inputs

  • Dmitry V. Zakablukov EMAIL logo
Published/Copyright: September 10, 2022

Abstract

Reversible circuits consisting of NOT, CNOT and 2-CNOT gates with small number of additional inputs are considered. For such a circuit implementing a map f:Z2nZ2n, we study the Shannon complexity function L(n, q) under the condition that the number of additional inputs is q = O(n2). For this range of q, it is shown that L(n,q)n2n/log2n. We show that L(n,q)n2n/log2(n+q) for all qn2nn/ϕ(n), where ϕ(n)andn/ϕ(n)log2nasn.


Note

Originally published in Diskretnaya Matematika (2021) 33,№3, 46–53 (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] Lupanov O. B., “On a method of synthesis of circuits”, Izv. vuzov. Radiofizika”, 1:1 (1958), 23–26 (in Russian).Search in Google Scholar

[3] Feynman R., “Quantum mechanical computers”, Optic News, 11:2 (1985), 11–20.10.1364/CLEO.1984.TUAA2Search in Google Scholar

[4] Toffoli T., “Reversible computing”, Automata, Languages and Programming, Lect. Notes Comput. Sci., 85, 1980, 632–644.10.1007/3-540-10003-2_104Search in Google Scholar

[5] Zakablukov D. V., “Gate complexity of reversible circuits as a measure of complexity of even permutations”, Vest. Bauman MGTU, ser. “Priborostroenie”, 1:100 (2015), 67–82 (in Russian).Search in Google Scholar

[6] 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

[7] Karpova N. A., “On calculations with limited memory”, Matematicheskie voprosy kibernetiki, 2 (1989), 131–144 (in Russian).Search in Google Scholar

[8] Zakablukov D. V., “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”, Discrete Math. Appl., 31:1 (2021), 61–75.10.1515/dma-2021-0006Search in Google Scholar

[9] Shende V. V., Prasad A. K., Markov I. L., Hayes J. P., “Synthesis of reversible logic circuits”, IEEE Trans. Computer-Aided Des. Integr. Circuits Systems, 22:6 (2006), 710–722.10.1109/TCAD.2003.811448Search in Google Scholar

[10] Shende V. V., Prasad A. K., Markov I. L., Hayes J. P., “Synthesis of reversible logic circuits”, IEEE Trans. Computer-Aided Des. Integr. Circuits Systems, 22:6 (2006), 710–722.10.1109/TCAD.2003.811448Search in Google Scholar

Received: 2021-05-18
Published Online: 2022-09-10
Published in Print: 2022-08-26

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 30.11.2025 from https://www.degruyterbrill.com/document/doi/10.1515/dma-2022-0023/html
Scroll to top button