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.

A New Pairwise NPN Boolean Matching Algorithm Based on Structural Difference Signature

“…Moore et al [21] presented an NPN Boolean matching algorithm using Walsh spectra. The authors of [22] utilized Haar spectra to check the equivalence of two logic circuits.…”

Minimization of Circuit Design Using Permutation of Haar Wavelet Series

“…8 In applications of non-normalized Haar functions in switching theory and logic design, [2][3][4][5][6]8,12,15,17 it is convenient to represent the discrete Haar functions in terms of switching variables corresponding to the rows of the basic Haar transform matrix as is shown in the following example.…”

“…The realization of the mcnc benchmark function con1 requires to store and work with 38 nonzero Haar coefficients. However, the optimization procedure reduces the number of coefficients to 12 for the ordering of indices, that corresponds to the following order of variables in f , x 3 , x 4 , x 7 , x 2 , x 1 , x 6 , and x 5 , which in this case, makes about 62% of saving in space for the Haar coefficients. Table 4 shows nonzero coefficients.…”

“…[1][2][3][4][5][6] In particular, the discrete Haar transform appears very interesting for its wavelets-like properties and fast calculation algorithms. The applications have been found in circuit synthesis, verification and testing.…”

“…The applications have been found in circuit synthesis, verification and testing. [1][2][3][4][5][6][7][8][9] For applications of the Haar transform in logic design, efficient ways of calculating the Haar spectrum from reduced forms of Boolean functions are needed. Recently, such methods were introduced for calculation of the Haar spectrum from disjoint cubes, 10,11 and different types of decision diagrams.…”