Efficient calculation of spectral coefficients and their applications

Spectral methods for analysis and design of digital logic circuits have been proposed and developed for several years. The widespread use of these techniques has suffered due to the associated computational complexity. This paper presents a new approach for the computation of spectral coefficients with polynomial complexity. Usually, the computation of the spectral coefficients involves the evaluation of inner products of vectors of exponential length. In the new approach, it is not necessary to compute inner products, rather, each spectral coefficient is expressed in terms of a measure of correlation between two Boolean functions. This formulation coupled with compact BDD representations of the functions reduces the overall complexity. Further, some computer aided design applications are presented that can make use of the new spectrum evaluation approach. In particular, the basis for a synthesis method that allows spectral coefficients to be computed in an iterative manner is outlined. The proposed synthesis approach has the advantage that it can accommodate a wide variety of constituent gates, including XOR gates, and complex subfunctions for realizing the circuits. >

[1]  Masahiro Fujita,et al.  Spectral Transforms for Large Boolean Functions with Applications to Technology Mapping , 1997, Formal Methods Syst. Des..

[2]  Albert R. Wang,et al.  Logic verification using binary decision diagrams in a logic synthesis environment , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.

[3]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[4]  Masahiro Fujita,et al.  Fast spectrum computation for logic functions using binary decision diagrams , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[5]  Jean-Pierre Deschamps,et al.  Discrete and switching functions , 1978 .

[6]  D. Michael Miller,et al.  Spectral Fault Signatures for Single Stuck-At Faults in Combinational Networks , 1984, IEEE Transactions on Computers.

[7]  Robert J. Lechner.  HARMONIC ANALYSIS OF SWITCHING FUNCTIONS , 1971 .

[8]  A. M. Lloyd,et al.  A consideration of orthogonal matrices, other than the Rademacher-Walsh types, for the synthesis of digital networks , 1979 .

[9]  C.R. Edwards.  The Application of the Rademacher–Walsh Transform to Boolean Function Classification and Threshold Logic Synthesis , 1975, IEEE Transactions on Computers.

[10]  Bogdan J. Falkowski,et al.  Calculation of the Rademacher-Walsh spectrum from a reduced representation of Boolean functions , 1992, Proceedings EURO-DAC '92: European Design Automation Conference.

[11]  Suku Nair,et al.  An iterative combinational logic synthesis technique using spectral information , 1993, Proceedings of EURO-DAC 93 and EURO-VHDL 93- European Design Automation Conference.

[12]  Marek Perkowski,et al.  Integration of logic synthesis and high-level synthesis into the DIADES design automation system , 1989, IEEE International Symposium on Circuits and Systems,.

[13]  Melvin A. Breuer,et al.  Probabilistic Aspects of Boolean Switching Functions via a New Transform , 1981, JACM.

[14]  Sharad C. Seth,et al.  An Analysis of the Use of Rademacher-Walsh Spectrum in Compact Testing , 1984, IEEE Trans. Computers.

[15]  Alfred K. Susskind,et al.  Testing by Verifying Walsh Coefficients , 1983, IEEE Transactions on Computers.

[16]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[17]  John L. Shanks,et al.  Computation of the Fast Walsh-Fourier Transform , 1969, IEEE Transactions on Computers.

[18]  C. R. Edwards.  The design of easily tested circuits using mapping and spectral techniques , 1977 .

[19]  E. A. Trachtenberg,et al.  Design automation tools for efficient implementation of logic functions by decomposition , 1989, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[20]  C. Y. Lee.  Representation of switching circuits by binary-decision programs , 1959 .

[21]  S. L. Hurst.  The Application of Chow Parameters and Rademacher Walsh Matrices in the Synthesis of Binary Functions , 1973, Comput. J..

[22]  Thyagaraju R. Damarla.  Generalized Transforms for Multiple Valued Circuits and Their Fault Detection , 1992, IEEE Trans. Computers.

[23]  C. K. Chow,et al.  On the characterization of threshold functions , 1961, SWCT.

[24]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[25]  Jacob A. Abraham,et al.  Probabilistic design verification , 1991, 1991 IEEE International Conference on Computer-Aided Design Digest of Technical Papers.

[26]  Edward J. McCluskey,et al.  Probabilistic Treatment of General Combinational Networks , 1975, IEEE Transactions on Computers.

[27]  Masahiro Fujita,et al.  Evaluation and improvement of Boolean comparison method based on binary decision diagrams , 1988, [1988] IEEE International Conference on Computer-Aided Design (ICCAD-89) Digest of Technical Papers.