NegaBent, No Regrets: Evolving Spectrally Flat Boolean Functions

TL;DR

This paper explores the use of evolutionary algorithms, particularly genetic programming, to generate negabent Boolean functions with flat spectral properties across various dimensions, demonstrating their effectiveness.

Contribution

It introduces an evolutionary approach to generate negabent Boolean functions, a class with optimal spectral properties, in both even and odd dimensions.

Findings

Genetic programming effectively evolves negabent functions.

Successful evolution of negabent functions across multiple dimensions.

Evolutionary algorithms are suitable for designing functions with specific spectral properties.

Abstract

Negabent Boolean functions are defined by having a flat magnitude spectrum under the nega-Hadamard transform. They exist in both even and odd dimensions, and the subclass of functions that are simultaneously bent and negabent (bent-negabent) has attracted interest due to the combined optimal periodic and negaperiodic spectral properties. In this work, we investigate how evolutionary algorithms can be used to evolve (bent-)negabent Boolean functions. Our experimental results indicate that evolutionary algorithms, especially genetic programming, are a suitable approach for evolving negabent Boolean functions, and we successfully evolve such functions in all dimensions we consider.