English

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 kk-automatic sets SS 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 jj such that SS forms an additive basis of order jj, 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}
}
R2 v1 2026-06-22T22:22:56.198Z