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VLSI Design
Volume 14 (2002), Issue 1, Pages 53-64

Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs

1Department of ECE, Mississippi State University, P.O. Box 9571, Mississippi, MS, USA
2Institute of Computer Science, University of Bremen, Bremen 28359, Germany
3Albert-Ludwigs-University, Freiburg, Germany

Received 20 January 2000; Revised 4 October 2000

Copyright © 2002 Hindawi Publishing Corporation. 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.


A probabilistic equivalence checking method is developed based on the use of partial Haar Spectral Diagrams (HSDs). Partial HSDs are defined and used to represent a subset of Haar spectral coefficients for two Boolean functions. The resulting coefficients are then used to compute and to iteratively refine the probability that two functions are equivalent. This problem has applications in both logic synthesis and verification. The method described here can be useful for the case where two candidate functions require extreme amounts of memory for a complete BDD representation. Experimental results are provided to validate the effectiveness of this approach.