A Minimal Substitution Basis for the Kalm\'ar Elementary Functions
Logic
2026-02-11 v5 Computational Complexity
Logic in Computer Science
Abstract
We show that the class of Kalm\'ar elementary functions can be inductively generated from the addition, the integer remainder, and the base-two exponentiation, hence improving previous results by Marchenkov and Mazzanti. We also prove that the substitution basis defined by these three operations is minimal. Furthermore, we discuss alternative substitution bases under arity constraints.
Cite
@article{arxiv.2505.23787,
title = {A Minimal Substitution Basis for the Kalm\'ar Elementary Functions},
author = {Mihai Prunescu and Lorenzo Sauras-Altuzarra and Joseph M. Shunia},
journal= {arXiv preprint arXiv:2505.23787},
year = {2026}
}
Comments
Revision includes minor changes