Abstract
The Walsh transform has numerous applications in computer-aided design, but the usefulness of these techniques in practice has been limited by the size of the boolean functions that can be transformed. Currently available techniques limit the functions to less than 20 variables. In this paper, we show how to compute concise representations of the Walsh transform for functions with several hundred variables. We have applied our techniques to boolean technology mapping and, in certain cases, we obtained a speed up of as much as 50% for the matching phase.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R.E. Bryant, "Graph-based algorithms for boolean function manipulation," IEEE Transactions on Computers, Vol. C-35, No. 8, 1986.
M.A. Harrison, Introduction to Switching and Automata Theory. McGraw-Hill, 1965.
S.L. Hurst, D.M. Miller, and J.C. Muzio, Spectral Techniques in Digital Logic. Academic Press, Inc., 1985.
R.J. Lechner, "A transform approach to logic design," IEEE Transactions on Computers, Vol. C-19, No. 7, 1970.
F. Mailhot and G. De Micheli, "Technology mapping using boolean matching and don't care sets," In Proceedings of the 1990 European Design Automation Conference, 1990.
G. De Micheli, David Ku, F. Mailhot, and T.K. Truong, "The olympus synthesis system for digital design," IEEE Design and Test of Computers, Oct. 1990.
J. Yang and G. De Micheli, "Spectral Techniques for Technology Mapping," Technical Report CSL-TR-91-498, Standford University, Dec. 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Clarke, E., Mcmillan, K., Zhao, X. et al. Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping. Formal Methods in System Design 10, 137–148 (1997). https://doi.org/10.1023/A:1008695706493
Issue Date:
DOI: https://doi.org/10.1023/A:1008695706493