- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Volume 2011 (2011), Article ID 356137, 9 pages
New Considerations for Spectral Classification of Boolean Switching Functions
1Department of Mathematics & Computer Science, University of Lethbridge, 4401 University Drive West, Lethbridge, AB, Canada T1K 3M4
2Department of Computer Science, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC, Canada V8W 3P6
Received 5 May 2010; Revised 21 October 2010; Accepted 11 January 2011
Academic Editor: Avi Ziv
Copyright © 2011 J. E. Rice et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- C. R. Edwards, “The application of the Rademacher-Walsh transform to Boolean function classification and threshold logic synthesis,” IEEE Transactions on Computers, vol. 24, no. 1, pp. 48–71, 1975.
- M. Karpovsky, Finite Orthogonal Series in the Design of Digital Devices, John Wiley & Sons, New York, NY, USA, 1976.
- S. L. Hurst, D. M. Miller, and J. C. Muzio, Spectral Techniques in Digital Logic, Academic Press, Orlando, Fla, USA, 1985.
- S. Hurst, The Logical Processing of Digital Signals, Crane Russak, 1978.
- J. E. Rice, Autocorrelation coefficients in the representation and classification of switching functions, Ph.D. thesis, University of Victoria, 2003.
- M. A. Thornton and R. Drechsler, “Computation of spectral information from logic netlists,” in Proceedings of the 30th IEEE International Symposium on Multiple-Valued Logic (ISMVL '00), pp. 53–58, May 2000.
- M. A. Thornton and V. S. S. Nair, “Efficient spectral coefficient calculation using circuit output probabilities,” Digital Signal Processing, vol. 4, no. 4, pp. 245–254, 1994.
- M. A. Thornton and V. S. S. Nair, “Efficient calculation of spectral coefficients and their applications,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 14, no. 11, pp. 1328–1341, 1995.
- A. Žužek, R. Drechsler, and M. A. Thornton, “Boolean function representation and spectral characterization using AND/OR graphs,” Integration, the VLSI Journal, vol. 29, no. 2, pp. 101–116, 2000.
- E. M. Clarke, K. L. McMillan, X. Zhao, M. Fujita, and J. Yang, “Spectral transforms for large Boolean functions with applications to technology mapping,” in Proceedings of the 30th ACM/IEEE Design Automation Conference, pp. 54–60, June 1993.
- D. Jankovic, R. S. Stankovic, and R. Drechsler, “Decision diagram method for calculation of pruned Walsh transform,” IEEE Transactions on Computers, vol. 50, no. 2, pp. 147–157, 2001.
- R. S. Stanković, M. Stanković, C. Moraga, and T. Sasao, “Calculation of Reed-Muller-Fourier coefficients of multiple-valued functions through multiple-place decision diagrams,” in Proceedings of the International Symposium on Multiple-Valued Logic (ISMVL '94), pp. 82–88, 1994.
- S. Purwar, “An efficient method of computing generalized Reed-Muller expansions from binary decision diagram,” IEEE Transactions on Computers, vol. 40, no. 11, pp. 1298–1301, 1991.
- M. A. Thornton and R. Drechsler, “Spectral decision diagrams using graph transformations,” in Proceedings of the Conference on Design, Automation, and Test in Europe (DATE '01), pp. 713–719, 2001.
- M. A. Thornton, “Mixed-radix MVL function spectral and decision diagram representation,” Automation and Remote Control, vol. 65, no. 6, pp. 1007–1017, 2004.
- B. J. Falkowski and T. Sasao, “Unified algorithm to generate Walsh functions in four different orderings and its programmable hardware implementations,” IEE Proceedings: Vision, Image and Signal Processing, vol. 152, no. 6, pp. 819–826, 2005.
- B. J. Falkowski, “Parallelization of methods to calculate Walsh spectra for logic functions,” Journal of Multiple-Valued Logic and Soft Computing, vol. 10, no. 2, pp. 91–127, 2004.
- J. P. Hansen and M. Sekine, “Synthesis by spectral translation using Boolean decision diagrams,” in Proceedings of the 33rd Annual Design Automation Conference, pp. 248–253, June 1996.
- J. Moore, K. Fazel, M. A. Thornton, and D. M. Miller, “Boolean function matching using Walsh spectral decision diagrams,” in IEEE Dallas ICAS Workshop on Design, Applications, Integration and Software (DCAS '06), pp. 127–130, Richardson, Tex, USA, October 2006.
- D. M. Miller, “Spectral and two-place decomposition techniques in reversible logic,” in Proceedings of the 45th Midwest Symposium on Circuits and Systems (MWSCAS '02), vol. 2, pp. 493–496, August 2002.
- D. M. Miller and G. W. Dueck, “Spectral techniques for reversible logic synthesis,” in Proceedings of the 6th International Symposium on Representations and Methodology of Future Computing Technologies, 2002.
- M. G. Karpovsky, R. S. Stanković, and C. Moraga, “Spectral techniques in binary and multiple-valued switching theory: a review of results in the decade 1991–2000,” Journal of Multiple-Valued Logic and Soft Computing, vol. 10, no. 3, pp. 261–286, 2004.
- M. A. Thornton, R. Drechsler, and D. M. Miller, Spectral Techniques in VLSI CAD, Kluwer Academic Publishers, 2001.
- B. J. Falkowski and S. Yan, “Properties of logic functions in spectral domain of sign Hadamard-Haar transform,” Journal of Multiple-Valued Logic and Soft Computing, vol. 11, no. 1-2, pp. 185–211, 2005.
- B. J. Falkowski and S. Yan, “Ternary Walsh transform and its operations for completely and incompletely specified Boolean functions,” IEEE Transactions on Circuits and Systems I, vol. 54, no. 8, pp. 1750–1764, 2007.
- C. C. Tsai and M. Marek-Sadowska, “Boolean functions classification via fixed polarity Reed-Muller forms,” IEEE Transactions on Computers, vol. 46, no. 2, pp. 173–186, 1997.
- A. B. Lapshin, “Classification of Boolean functions by the invariants of their matrix representation,” Automation and Remote Control, vol. 67, no. 7, pp. 1100–1107, 2006.
- J. E. Rice and J. C. Muzio, “Use of the autocorrelation function in the classification of switching functions,” in Proceedings of the Euromicro Symposium on Digital System Design: Architectures, Methods and Tools (DSD '02), pp. 244–251, 2002.
- I. Strazdins, “Universal affine classification of Boolean functions,” Acta Applicandae Mathematicae, vol. 46, no. 2, pp. 147–167, 1997.
- N. Anderson, The classification of Boolean functions using the Rademacher-Walsh transform, M.S. thesis, University of Victoria, 2007.
- Maplesoft, “Maple 10,” 2007, http://www.maplesoft.com/products/maple/history/documentation.aspx.