Computation of the Fast Walsh-Fourier Transform
IEEE Transactions on Computers
On the characterization of threshold functions
FOCS '61 Proceedings of the 2nd Annual Symposium on Switching Circuit Theory and Logical Design (SWCT 1961)
Composite Spectra and the Analysis of Switching Circuits
IEEE Transactions on Computers
A Digital Synthesis Procedure Under Function Symmetries and Mapping Methods
IEEE Transactions on Computers
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Five operations are defined in the Rademacher-Walsh transform domain. It is shown that these operations allow Boolean functions to be classified in a very concise way. The result of applying this classification to Boolean functions of up to fourth order indicates that threshold functions play an important part in the composition of Boolean functions. A synthesis method is developed for the synthesis of any Boolean function using, as a basic element, an "optimized universal threshold logic gate." This gate overcomes the analog threshold tolerancing problems encountered in other threshold gate designs and is readily fabricated in an integrated circuit form. The use of this gate in logic design is expected to provide a considerable cost-saving over conventional methods.