Logic Circuit Equivalence Checking Using Haar Spectral Coefficients and Partial BDDs

Abstract

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.