Hybrid Reed-Muller Haar Transform and its Application in Reduction the Spectral Representations of Logic Functions

In this paper we present a new hybrid transform based on the Kronecker product of Reed-Muller and Reed-Muller Haar transforms. The proposed transform shares attractive properties of both Reed-Muller transform and Reed-Muller Haar transform. An example of application of hybrid transform for reduction of the number of nonzero coefficients in spectra of truth vectors of switching functions is presented. The experiments show that the proposed approach, on average, reduces the number of nonzero coefficients in the spectra of benchmark functions.

[1]  B.J. Falkowski,et al.  Generalized multi-polarity Haar transform , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[2]  P. Yip,et al.  Rationalized Hadamard-haar Transform , 1977 .

[3]  M. Karpovsky,et al.  Detection of stuck-at and bridging faults in Reed-Muller canonical (RMC) networks , 1989 .

[4]  E. A. Trachtenberg,et al.  Efficient Spectral Techniques for Logic Synthesis , 1993 .

[5]  Jaakko Astola,et al.  Advances in Signal Transforms: Theory and Applications , 2007 .

[6]  D. Green.  Reed-Muller expansions with fixed and mixed polarities over GF(4) , 1990 .

[7]  Tsutomu Sasao,et al.  Switching Theory for Logic Synthesis , 1999, Springer US.

[8]  Marek A. Perkowski,et al.  Generalized Partially-Mixed-Polarity Reed-Muller Expansionand Its Fast Computation , 1996, IEEE Trans. Computers.

[9]  J. Astola,et al.  Binary polynomial transforms and nonlinear digital filters , 1995 .

[10]  Sos S. Agaian,et al.  Parameterisation of slant-Haar transforms , 2003 .

[11]  Jaakko Astola,et al.  Tree-Structured Haar Transforms , 2004, Journal of Mathematical Imaging and Vision.

[12]  Tsutomu Sasao,et al.  Logic Synthesis and Optimization , 1997 .

[13]  Mark G. Karpovsky,et al.  Spectral Techniques and Fault Detection , 1985 .

[14]  K. R. Rao,et al.  Image Data Processing by Hadamard-Haar Transform , 1975, IEEE Transactions on Computers.

[15]  Claudio Moraga,et al.  Design of Haar wavelet transforms and Haar spectral transform decision diagrams for multiple-valued functions , 2001, Proceedings 31st IEEE International Symposium on Multiple-Valued Logic.

[16]  Shixing Yan,et al.  Properties and relations for hybrid multi-polarity arithmetic-Walsh transform , 2005, 48th Midwest Symposium on Circuits and Systems, 2005..

[17]  Elena Dubrova,et al.  Testability of generalized multiple-valued Reed-Muller circuits , 1996, Proceedings of 26th IEEE International Symposium on Multiple-Valued Logic (ISMVL'96).

[18]  T. R. Damarla.  Fault detection in Reed-Muller canonical (RMC) networks , 1989, Proceedings. IEEE Energy and Information Technologies in the Southeast'.

[19]  Elena Dubrova,et al.  Easily Testable Multiple-Valued Logic Circuits Derived from Reed-Muller Circuits , 2000, IEEE Trans. Computers.