Heuristic algorithms for obtaining Polynomial Threshold Functions with low densities

TL;DR

This paper introduces heuristic algorithms, including a genetic algorithm, to find polynomial threshold functions with minimal monomials for Boolean functions, outperforming existing methods in producing sparse representations.

Contribution

It presents new heuristic algorithms, notably a genetic algorithm, that improve the sparsity of polynomial threshold functions compared to previous approaches.

Findings

Heuristic algorithms outperform non-heuristic methods in finding sparse PTFs.

Genetic Algorithm shows superior performance in reducing the number of monomials.

Results demonstrate improved efficiency and parsimony in Boolean function representations.

Abstract

In this paper we present several heuristic algorithms, including a Genetic Algorithm (GA), for obtaining polynomial threshold function (PTF) representations of Boolean functions (BFs) with small number of monomials. We compare these among each other and against the algorithm of Oztop via computational experiments. The results indicate that our heuristic algorithms find more parsimonious representations compared to the those of non-heuristic and GA-based algorithms.