Abstract
Reversible computing basically means computation with less or not at all electrical power. Since the standard binary gates are not usually reversible we use the Fredkin gate in order to achieve reversibility. An algorithm for designing reversible digital circuits is described in this paper. The algorithm is based on Multi Expression Programming (MEP), a Genetic Programming variant with a linear representation of individuals. The case of digital circuits for the even-parity problem is investigated. Numerical experiments show that the MEP-based algorithm is able to easily design reversible digital circuits for up to the even-8-parity problem.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bellman, R.: Dynamic Programming. Princeton University Press, New Jersey (1957)
Bennett, C.H., Landauer, R.: Fundamental physical limits of computation. Scientific American 253, 48–56 (1985)
Fredkin, E., Toffoli, T.: Conservative logic. International Journal of Theoretical Physics 21, 219–253 (1982)
Klein, J.P., Leete, T.H., Rubin, H.: A Biomolecular Implementation of Logically Reversible Computation with Minimal Energy Dissipation. BioSystems 52, 15–23 (1999)
Koza, J.R.: Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge (1992)
Koza, J.R.: Genetic Programming II: Automatic Discovery of Reusable Subprograms. MIT Press, Cambridge (1994)
Landauer, R.: Irreversibility and heat generation in the computing process. IBM Journal of Research and Development 5, 183–191 (1961)
Langdon, W.B.: The Distribution of Reversible Functions is Normal. In: Riolo, R.L., Worzel, B. (eds.) Genetic Programming Theory and Practise, pp. 173–188. Kluwer Academic Publishers, Dordrecht (2003)
Merkle, R.C.: Reversible Electronic Logic Using Switches. Nanotechnology 4, 21–40 (1993)
Oltean, M.: Solving Even-parity problems with Multi Expression Programming. In: Chen, K., et al. (eds.) The 8th International Conference on Computation Sciences, North Carolina, pp. 315–318 (2003)
Oltean, M., Grosan, C.: Evolving Digital Circuits using Multi Expression Programming. In: Zebulum, R., Gwaltney, D., Horbny, G., Keymeulen, D., Lohn, J., Stoica, A. (eds.) NASA/DoD Conference on Evolvable Hardware, Seattle, June 24-26, pp. 87–90. IEEE Press, NJ (2004)
Oltean, M.: Improving Multi Expression Programming: an Ascending Trail from Sea-level Even-3-parity Problem to Alpine Even-18-Parity Problem. In: Nedjah, N., et al. (eds.) Evolutionary Machine Design, contributed ch. 15. Studies in Soft Computing and Fuzziness, vol. 161, pp. 229–255. Springer, Heidelberg (2004)
Miller, J.F., Job, D., Vassilev, V.K.: Principles in the Evolutionary Design of Digital Circuits - Part I. Genetic Programming and Evolvable Machines 1(1), 7–35 (2000)
Poli, R., Page, J.: Solving High-Order Boolean Parity Problems with Smooth Uniform Crossover, Sub-Machine Code GP and Demes. Journal of Genetic Programming and Evolvable Machines, 1–21 (2000)
Syswerda, G.: Uniform Crossover in Genetic Algorithms. In: Schaffer, J.D. (ed.) Proceedings of the 3rd International Conference on Genetic Algorithms, pp. 2–9. Morgan Kaufmann Publishers, San Mateo (1989)
Toffoli, T.: Reversible computing. In: de Bakker, J.W., van Leeuwen, J. (eds.) Automata, Languages and Programming, 7th Colloquium. LNCS, vol. 75, pp. 632–644. Springer, Heidelberg (1980)
Wolpert, D.H., McReady, W.G.: No Free Lunch Theorems for Search, Technical Report, SFI-TR-05-010, Santa Fe Institute (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Oltean, M. (2005). Evolving Reversible Circuits for the Even-Parity Problem. In: Rothlauf, F., et al. Applications of Evolutionary Computing. EvoWorkshops 2005. Lecture Notes in Computer Science, vol 3449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-32003-6_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-32003-6_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25396-9
Online ISBN: 978-3-540-32003-6
eBook Packages: Computer ScienceComputer Science (R0)