On polynomial growth functions of D0L-systems

TL;DR

This paper proves that any polynomial function mapping natural numbers to positive integers can be realized as the growth function of a D0L-system, expanding understanding of the possible growth behaviors of these systems.

Contribution

It establishes that all polynomial functions are achievable as growth functions of D0L-systems, providing a complete characterization of their polynomial growth behaviors.

Findings

Every polynomial function is realizable as a D0L-system growth function.

The paper characterizes the relationship between polynomial functions and D0L-system growth.

It broadens the understanding of growth functions in formal language systems.

Abstract

The aim of this paper is to prove that every polynomial function that maps the natural integers to the positive integers is the growth function of some D0L-system.