We investigate one of the most basic problems in streaming algorithms: approximating the number of elements in the stream. In 1978, Morris famously gave a randomized algorithm achieving a constant-factor approximation error for streams of length at most N in space $O(\log \log N)$. We investigate the pseudo-deterministic complexity of the problem and prove a tight $\Omega(\log N)$ lower bound, thus resolving a problem of Goldwasser-Grossman-Mohanty-Woodruff.

翻译：我们研究流算法中最基本的问题之一：近似计算流中元素的数量。1978年，Morris 提出了一个著名的随机算法，对于长度不超过 N 的流，在空间 $O(\log \log N)$ 内实现了常数因子近似误差。我们研究了该问题的伪确定性复杂度，并证明了紧致的 $\Omega(\log N)$ 下界，由此解决了 Goldwasser-Grossman-Mohanty-Woodruff 提出的问题。