Abstract
Spectral methods have been used for logic design for many years. However, their use was limited to the synthesis and optimization of small digital circuits, due to the enormous complexity in computing the spectra of large logic functions. Recent developments in design automation and logic synthesis have prompted a new look at these methods, with emphasis on developing efficient computational procedures so that these powerful but complex methods can be used for the synthesis and optimization of larger logic networks. In this article we review the fundamentals of spectral design methods and present some new techniques that make application of such techniques to practical problems feasible.
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References
S.B.Aker “Binary decision diagrams” IEEE Trans. Comput. Vol. C-27. No. 6, June 1978, pp. 509–516.
R.L.Ashenhurst “The decomposition of switching functions,”in Proceedings of an International Symposium on the Theory of Switching pp. 74–116, April 1957.
Ph. W. Besslich and E. A. Trachtenberg, “A three-valued quasi-linear transformation for logic synthesis”, in Spectral techniques: Theory and applications, Ed. C. Moraga and R. Creutzburg, Elsevier, North Holland, 1992.
Ph. B. Besslich “On the Walsh-Hadamard transform and prime implicant extraction”, IEEE Trans. Electromagnetic Compat Vol. EMC-20, No. 4, Nov. 1978, pp. 516–519.
R. K. Brayton et.al., Logic minimization algorithms for VLSI synthesis, Kluwer Academic, Boston, 1984.
R.E.Bryant “Graph-based algorithms for Boolean function manipulation,” IEEE Trans. Comput. Vol. C-35, No. 8 Aug. 1986, pp. 677–691.
T. Damarla and M. G. Karpovsky, “Reed-Muller spectral techniques for fault detection”, Second international workshop on spectral techniques, Ecole Polytechnique de Montreal, Canada, Oct. 1986.
N.DiToro The sign transform’s application to fault detection in digital circuits and its efficient implementation, Master’s Thesis, Drexel University, Philadelphia, March 1991.
K.D.Heidtmann “Arithmetic spectrum applied to fault detection for combinational networks” IEEE Trans. on Computers Vol. 40, No. 3, March 1991, pp. 320–324.
S. L. Hurst, D. M. Miller and J. C. Muzio, Spectral techniques in digital logic, Academic Press, London, 1985.
M. G. Karpovsky, Finite orthogonal series in the design of digital devices, John Wiley, New York, 1976.
M. G. Karpovsky, Ed., Spectral techniques and fault detection, Academic Press, Orlando, 1985.
R. Lechner, “Harmonic analysis of switching functions”, in Recent developments in switching theory, A. Mukhopadhyay, Ed., Academic Press, New York, 1971, pp. 121–228.
P. Nagajara and M. G. Karpovsky, “Optimal robust compression of test responses”, IEEE Trans. Computers, Vol. 39, No. 1, Jan. 1990, pp. 138–141.
S.M.Reddy “Easily testable realizations for logic functions”IEEE Trans. Com puters Vol. C-21, Nov. 1972, pp. 1183–1188.
V.M.Tokmen “Disjoint decomposability of multiple valued functions by spectral means”,in Proc. IEEE 10th Int. Symp. Mult. Valued Logic 1980, pp. 88–93.
D. Varma and E. A. Trachtenberg, “A fast algorithm for the optimal state assignment of large finite state machines”, in ICCAD Dig. Tech. Papers, Santa Clara, CA, 1988, pp. 152–155.
D. Varma and E. A. Trachtenberg, “Design automation tools for efficient implementation of logic functions by decomposition,” IEEE Transactions on CAD, CAD-8, Aug. 1989, pp. 901–916.
D.Varma and E.A.Trachtenberg Trachtenberg, “On the estimation of logic complexity for design automation applications”, in Proc. ICCD,New York, 1990.
D. Varma and E. A. Trachtenberg, “Computation of Reed-Muller expansions of incompletely specified Boolean functions from reduced representations,” IEE Proceedings-E, Vol. 138, No. 2, March 1991, pp. 85–92.
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© 1993 Springer Science+Business Media New York
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Varma, D., Trachtenberg, E.A. (1993). Efficient Spectral Techniques for Logic Synthesis. In: Sasao, T. (eds) Logic Synthesis and Optimization. The Kluwer International Series in Engineering and Computer Science, vol 212. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-3154-8_10
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DOI: https://doi.org/10.1007/978-1-4615-3154-8_10
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