We prove an essentially sharp $\tilde \Omega (n/k)$ lower bound on the k-round distributional complexity of the k-step pointer chasing problem under the uniform distribution, when Bob speaks first. This is an improvement over Nisan and Wigderson’s $\tilde \Omega (n/{k^2})$ lower bound, and essentially matches the randomized lower bound proved by Klauck. The proof is information-theoretic, and a key part of it is using asymmetric triangular discrimination instead of total variation distance; this idea may be useful elsewhere.

中文翻译：

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通过三角判别追踪指针

我们证明了一个本质上锋利的$\波浪号 \Omega (n/k)$的下限ķ- 的轮分布复杂度ķ- 当 Bob 先说话时，均匀分布下的步指针追逐问题。这是对 Nisan 和 Wigderson 的改进$\波浪号 \Omega (n/{k^2})$下界，并且基本上与 Klauck 证明的随机下界相匹配。该证明是信息论的，其关键部分是使用非对称三角判别而不是总变异距离；这个想法可能在其他地方有用。