The Space Complexity of Generating Tent Codes

Naoaki Okada; Shuji Kijima

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arXiv · 2310.14185

The Space Complexity of Generating Tent Codes

Naoaki Okada·Shuji Kijima

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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 $n$-th bit of a bit sequence generated by a chaotic map, such as $\beta$-expansion, tent map and logistic map in $o(n)$ 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 $n$-bits with an initial condition uniformly at random is exactly generated in $O(\log^2 n)$ space in expectation.

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Naoaki Okada, Shuji Kijima. 2023-10-22. The Space Complexity of Generating Tent Codes. https://arxiv.org/abs/2310.14185

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