Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Interpolating polynomials from their values
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Interpolation and approximation of sparse multivariate polynomials over GF(2)
SIAM Journal on Computing
Boolean Matrix Transforms for the Minimization of Modulo-2 Canonical Expansions
IEEE Transactions on Computers
Heuristic minimization of BDDs using don't cares
DAC '94 Proceedings of the 31st annual Design Automation Conference
A Multiple-Valued Reed-Muller Transform for Incompletely Specified Functions
IEEE Transactions on Computers
A Transform for Logic Networks
IEEE Transactions on Computers
A Theory of Galois Switching Functions
IEEE Transactions on Computers
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Abstract: In this paper we investigate the possibility of exploiting incompletely specified functions for the purpose of minimizing Reed-Muller (RM) forms. All the previous work in this area has been based on exhaustive search for the optimal solution, or on some approximations to it. Here we show that an alternative approach can bring better results: the definition of the MVL RM transforms as a polynomial interpolation over a finite field allows us to use the methods for sparse polynomial interpolation to find good approximations to the optimal solution. Starting from the general MVL case, we derive a computationally efficient algorithm for computing RM transforms for binary functions as well. We show empirically that the new method performs better than all known methods.