Efficient signatures with linear space complexity for detecting Boolean function equivalence

Abstract

A novel technique for generating efficient signatures has been proposed for characterizing Boolean functions. The computed signatures can be found to be insensitive to permutations of input variables. Such a signature can be used to find a match for a given function in a large library of Boolean functions. This paper utilizes the concept of A-transform used to solve the problem of probabilistic design verification. It has been proved analytically that for number of variables less than 5, the generated signature is unique. Randomly generated functions of 5, 6, and 7 variables, aliasing has been observed to be within 0.5%. This basic scheme is next modified to arrive at a signature with linear space complexity. The efficiency of the modified signature to distinguish nonequivalent Boolean functions can be found to be above 0.99 for Actel type multiplexor based FPGAs.