Reduction of variables of index generation functions using linear and quadratic transformations

Abstract

In many applications in communication, data retrieval and processing, digital system design, and related areas, incompletely specified switching (Boolean or multiple-valued) functions are encountered. A particular class of highly incompletely specified functions are the so-called index generation functions, which being defined on a small fraction of input combinations, often do not require all the variables to be represented. Reducing the variables of index generation functions is an important task, since they are used mainly in real-time applications and compactness of their representations influences performances of related systems. One approach towards reducing the number of variables in index generation functions are linear transformations meaning that initial variables are replaced by their linear combinations. A drawback is that finding an optimal transformation can be difficult. Therefore, in this paper, we first formulate the problem of finding a good linear transformation by using linear subspaces. This formulation serves as a basis to propose non-linear (polynomial) transformations to reduce the number of variables in index generation functions.