When is an automatic set an additive basis?
Number Theory
2017-10-24 v1 Discrete Mathematics
Formal Languages and Automata Theory
Combinatorics
Abstract
We characterize those -automatic sets of natural numbers that form an additive basis for the natural numbers, and we show that this characterization is effective. In addition, we give an algorithm to determine the smallest such that forms an additive basis of order , if it exists.
Cite
@article{arxiv.1710.08353,
title = {When is an automatic set an additive basis?},
author = {Jason Bell and Kathryn Hare and Jeffrey Shallit},
journal= {arXiv preprint arXiv:1710.08353},
year = {2017}
}