A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence

Naoaki Okada; Shuji Kijima

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arXiv · 2405.00327

A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence

Naoaki Okada·Shuji Kijima

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Abstract

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.

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Naoaki Okada, Shuji Kijima. 2024-05-01. A Smoothed Analysis of the Space Complexity of Computing a Chaotic Sequence. https://arxiv.org/abs/2405.00327

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