Multiple-valued generalized Reed-Muller forms

Abstract

The concept of canonical multiple-valued input generalized Reed-Muller forms (MIGRM), a direct extension of the well-known generalized Reed-Muller (GRM) forms for the logic with multiple-valued inputs, is introduced. Code normalization of single multiple-valued literals (MV-literal) to perform a final transformation is developed. The code normalization is used to make the transformation of the complete function independent on the polarity chosen. This simplifies and speeds up the main transformation step to the final restricted MIGRM form for the transformed single MV-literal. A computer program to realize the MIGRM transform for Boolean functions has been implemented. The direct circuit realization of MIGRMs as AND- EXOR programmable logic arrays with input decoders has excellent testability properties; they have applications to synthesis of other kinds of circuits with EXOR gates, such as the exclusive sums of products (ESOP), and they have image processing capabilities.<>