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Using group theory in reversible computing

Yvan Van Rentergem, Alexis De Vos UGent and Koen De Keyser UGent (2006) IEEE Congress on Evolutionary Computation. p.2382-2389
abstract
The (2(w))! reversible transformations on w wires, i.e. reversible logic circuits with w inputs and w outputs, together with the action of cascading, form a group, isomorphic to the symmetric group Sew. Therefore, we investigate the group S. as well as one of its subgroups isomorphic to S-n/2 x S-n/2. We then consider the left cosets, the right cosets, and the double cosets generated by the subgroup. Each element of a coset can function as the representative of the coset. Different choices of the coset space and different choices of the coset representatives lead to four different syntheses for implementing an arbitrary reversible logic operation into hardware. Comparison leads to a best choice: a single coset space, with representatives that are generalized TOFFOLI and FREDKIN gates.
Please use this url to cite or link to this publication:
author
organization
year
type
conference
publication status
published
subject
in
IEEE Congress on Evolutionary Computation
issue title
2006 IEEE CONGRESS ON EVOLUTIONARY COMPUTATION, VOLS 1-6
pages
2382 - 2389
publisher
IEEE
place of publication
New York, NY, USA
conference name
IEEE Congress on Evolutionary Computation (CEC 2006)
conference location
Vancouver, BC, Canada
conference start
2006-07-16
conference end
2006-07-21
Web of Science type
Article
Web of Science id
000245414204023
ISBN
9780780394872
DOI
10.1109/CEC.2006.1688605
language
English
UGent publication?
yes
classification
P1
additional info
pagination according to IEEE Explore: 2397-2404
id
411721
handle
http://hdl.handle.net/1854/LU-411721
date created
2008-05-20 22:07:00
date last changed
2010-10-14 09:50:43
@inproceedings{411721,
  abstract     = {The (2(w))! reversible transformations on w wires, i.e. reversible logic circuits with w inputs and w outputs, together with the action of cascading, form a group, isomorphic to the symmetric group Sew. Therefore, we investigate the group S. as well as one of its subgroups isomorphic to S-n/2 x S-n/2. We then consider the left cosets, the right cosets, and the double cosets generated by the subgroup. Each element of a coset can function as the representative of the coset. Different choices of the coset space and different choices of the coset representatives lead to four different syntheses for implementing an arbitrary reversible logic operation into hardware. Comparison leads to a best choice: a single coset space, with representatives that are generalized TOFFOLI and FREDKIN gates.},
  author       = {Van Rentergem, Yvan and De Vos, Alexis and De Keyser, Koen},
  booktitle    = {IEEE Congress on Evolutionary Computation},
  isbn         = {9780780394872},
  language     = {eng},
  location     = {Vancouver, BC, Canada},
  pages        = {2382--2389},
  publisher    = {IEEE},
  title        = {Using group theory in reversible computing},
  url          = {http://dx.doi.org/10.1109/CEC.2006.1688605},
  year         = {2006},
}

Chicago
Van Rentergem, Yvan, Alexis De Vos, and Koen De Keyser. 2006. “Using Group Theory in Reversible Computing.” In IEEE Congress on Evolutionary Computation, 2382–2389. New York, NY, USA: IEEE.
APA
Van Rentergem, Y., De Vos, A., & De Keyser, K. (2006). Using group theory in reversible computing. IEEE Congress on Evolutionary Computation (pp. 2382–2389). Presented at the IEEE Congress on Evolutionary Computation (CEC 2006), New York, NY, USA: IEEE.
Vancouver
1.
Van Rentergem Y, De Vos A, De Keyser K. Using group theory in reversible computing. IEEE Congress on Evolutionary Computation. New York, NY, USA: IEEE; 2006. p. 2382–9.
MLA
Van Rentergem, Yvan, Alexis De Vos, and Koen De Keyser. “Using Group Theory in Reversible Computing.” IEEE Congress on Evolutionary Computation. New York, NY, USA: IEEE, 2006. 2382–2389. Print.