Index Generation Functions Based on Linear and Polynomial Transformations

Abstract

Index generation functions are a particular class of switching (Boolean or multiple-valued) functions that have some important applications in communication, data retrieval and processing, and related areas. For these applications, determining compact representations of index generation functions is an important task. An approach towards this is to perform a linear transformation to reduce the number of required variables, but finding an optimal transformation can be difficult. In this paper, we propose non-linear transformations to reduce the number of variables, and formulate the problem of finding a good linear transformation using linear subspaces. Extending the set of initial variables by products of variables makes it easier to find a compact representation as the number of suitable transformations becomes larger.