A Method for Approximate Equivalence Checking

An approximate 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 the Haar spectral coefficients for two functions. Due to the uniqueness properties of the Haar transform, a necessary condition for equivalence is that the individual coefficients must have the same value. The probability that two functions are equivalent is then computed based on the number of observed, same-valued, Haar coefficients. The method described here can be useful for the case where two candidate functions require extreme amounts of computational resources for exact equivalence checking. For simplicity, the technique is explained for the binary case first and extensions to Multiple Valued Logic (MVL) are shown afterwards. Experimental results are provided to validate the effectiveness of this approach.