English

The Space Complexity of Generating Tent Codes

Computational Complexity 2023-10-24 v1

Abstract

This paper is motivated by a question whether it is possible to calculate a chaotic sequence efficiently, e.g., is it possible to get the nn-th bit of a bit sequence generated by a chaotic map, such as β\beta-expansion, tent map and logistic map in o(n)o(n) time/space? This paper gives an affirmative answer to the question about the space complexity of a tent map. We prove that a tent code of nn-bits with an initial condition uniformly at random is exactly generated in O(log2n)O(\log^2 n) space in expectation.

Cite

@article{arxiv.2310.14185,
  title  = {The Space Complexity of Generating Tent Codes},
  author = {Naoaki Okada and Shuji Kijima},
  journal= {arXiv preprint arXiv:2310.14185},
  year   = {2023}
}
R2 v1 2026-06-28T12:57:53.658Z