Permutation Algebra for Constructing Reversible Circuits

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References

[1] J. F. Humphreys, “A Course in Group Theory,” 5th Edition, Oxford University Press, Oxford, 1996.

[2] T. Taffoli, “Reversible Computing,” Proceedings of the 7th Colloquium on Automata, Languages and Programming, Vol. 85, 1980, pp. 632-644.
doi:10.1007/3-540-10003-2_104

[3] E. Fredkin and T. Taffoli, “Conservative Logic,” International Journal of Theoretical Physics, Vol. 21, No. 3-4, 1982, pp. 219-253. doi:10.1007/BF01857727

[4] A. Peres, “Reversible Logic and Quantum Computers,” Physical Review A, Vol. 32, No. 6, 1985, pp. 3266-3276.
doi:10.1103/PhysRevA.32.3266

[5] A. Barenco, C. H. Bennett, C. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin and H. Weinfurter, “Elementary Gates for Quantum Computation,” Physical Review A, Vol. 52, No. 5, 1995, pp. 3457-3467. doi:10.1103/PhysRevA.52.3457