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.

翻译：本文受以下问题启发：是否可能高效计算混沌序列，例如，能否在 $\mathrm{o}(n)$ 时间/空间内获取由混沌映射（如 $\beta$-展开、帐篷映射和逻辑斯蒂映射）生成的比特序列的第 $n$ 位？本文对帐篷映射的空间复杂度问题给出了肯定回答。我们证明，在平滑复杂度的意义上，给定比特序列是否为有效帐篷编码的判定问题可在 $\mathrm{O}(\log^{2} n)$ 空间内解决。