Decision diagram based techniques for the Haar wavelet transform

This paper describes a new data structure called the "Haar Spectral Diagram" (or HSD) useful for representing the Haar spectrum of Boolean functions. An alternative ordering of Haar coefficients is used to represent the Haar transform matrix in terms of a Kronecker product yielding a natural decision-diagram based representation. The resulting graph is a point-decomposition of the Haar spectrum using "0-element" edge values. For incompletely specified functions, the Haar spectrum represented as an HSD is shown to require no more nodes than the ROBDD for the same function, and for completely specified functions, the HSD is shown to be isomorphic to the ROBDD.

[1]  Stanley L. Hurst,et al.  Spectral techniques in digital logic , 1985 .

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

[3]  Randal E. Bryant,et al.  Efficient implementation of a BDD package , 1991, DAC '90.

[4]  Chip-Hong Chang,et al.  A novel paired Haar based transform: algorithms and interpretations in Boolean domain , 1993, Proceedings of 36th Midwest Symposium on Circuits and Systems.

[5]  Bogdan J. Falkowski,et al.  Efficient Algorithms for Forward and Inverse Transformations between Haar Spectrum and Binary Decisi , 1994, Proceeding of 13th IEEE Annual International Phoenix Conference on Computers and Communications.

[6]  Chip-Hong Chang,et al.  Efficient algorithms for the calculation of arithmetic spectrum from OBDD and synthesis of OBDD from arithmetic spectrum for incompletely specified Boolean functions , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[7]  Chip-Hong Chang,et al.  Efficient algorithms for the calculation of Walsh spectrum from OBDD and synthesis of OBDD from Walsh spectrum for incompletely specified Boolean functions , 1994, Proceedings of 1994 37th Midwest Symposium on Circuits and Systems.

[8]  Susanto Rahardja,et al.  Sign Haar Transform , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[9]  Radomir S. Stankovic.  Some remarks about spectral transform interpretation of MTBDDs and EVBDDs , 1995, ASP-DAC '95.

[10]  M. Sekine,et al.  Synthesis by spectral translation using Boolean decision diagrams , 1996, 33rd Design Automation Conference Proceedings, 1996.

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