A fast algorithm to minimize multi-output mixed-polarity generalized Reed-Muller forms

A very fast computer program that accepts a Boolean function as an array of multi-output disjoint cubes and returns a mixed-polarity Generalized Reed-Muller Form is presented. Such circuits often have gates and interconnections than classical sum-of-product realizations and are easily testable. The program was tested on many examples from literature as well as on many large arithmetic functions with up to 8 inputs, 8 output and 255 minterms. On all the examples from the literature the solutions were either the same or better than those generated by other methods. The algorithm is based on a new cube operation, called xlinking, that generalizes known operations of merger, exclusion and other logic operations specified by previous authors.

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