A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence
<|reference_start|>A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence: This work is motivated by a question whether it is possible to calculate a chaotic sequence efficiently, e.g., is it possible to get the $n$-th bit of a bit sequence generated by a chaotic map, such as $\beta$-expansion, tent map and logistic map in $\mathrm{o}(n)$ time/space? This paper gives an affirmative answer to the question about the space complexity of a tent map. We show that the decision problem of whether a given bit sequence is a valid tent code is solved in $\mathrm{O}(\log^{2} n)$ space in a sense of the smoothed complexity.<|reference_end|>
@article{okada2024a,
    title={A Smoothed Analysis of the Space Complexity of Computing a Chaotic
  Sequence},
    author={Naoaki Okada and Shuji Kijima},
    journal={arXiv preprint arXiv:2405.00327},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.00327},
    primaryClass={cs.CC}
}