Properties of Rotational Symmetric multiple valued functions and their Reed-Muller-Fourier spectra

TL;DR

This paper extends the concept of rotation symmetric functions to the multiple-valued domain, demonstrating their spectral properties and providing methods for their compact representation and spectrum calculation.

Contribution

It introduces the extension of rotation symmetric functions to the MV domain and presents a method to compute their Reed-Muller-Fourier spectra from compact representations.

Findings

Spectral symmetry is preserved in the Reed-Muller-Fourier spectrum.

Compact vector representations effectively describe MV rotation symmetric functions.

Method demonstrated with 3-valued and 4-valued functions.

Abstract

The concept of rotation symmetric functions from the Boolean domain is extended to the multiple-valued (MV) domain. It is shown that symmetric functions are a subset of the rotation symmetric functions. Functions exhibiting these kinds of symmetry may be given a compact value vector representation. It is shown that the Reed-Muller-Fourier spectrum of a function preserves the kind of symmetry and therefore it may be given a compact vector representation of the same length as the compact value vector of the corresponding function. A method is presented for calculating the RMF spectrum of symmetric and rotation symmetric functions from their compact representations. Examples are given for 3-valued and 4-valued functions.