English

A note on the complexity of addition

Computational Complexity 2023-06-16 v1

Abstract

We show that the sum of a sequence of integers can be computed in linear time on a Turing machine. In particular, the most obvious algorithm for this problem, which appears to require quadratic time due to carry propagation, actually runs in linear time by amortized analysis.

Keywords

Cite

@article{arxiv.2306.08513,
  title  = {A note on the complexity of addition},
  author = {Emil Jeřábek},
  journal= {arXiv preprint arXiv:2306.08513},
  year   = {2023}
}

Comments

5 pages

R2 v1 2026-06-28T11:05:02.188Z